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Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry

P-adic Deterministic and Random Dynamics (Paperback, Softcover reprint of hardcover 1st ed. 2004): Andrei Y. Khrennikov, Marcus... P-adic Deterministic and Random Dynamics (Paperback, Softcover reprint of hardcover 1st ed. 2004)
Andrei Y. Khrennikov, Marcus Nilsson
R2,884 Discovery Miles 28 840 Ships in 10 - 15 working days

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

Algebraic K-Theory (Paperback, Softcover reprint of hardcover 1st ed. 1995): Hvedri Inassaridze Algebraic K-Theory (Paperback, Softcover reprint of hardcover 1st ed. 1995)
Hvedri Inassaridze
R4,394 Discovery Miles 43 940 Ships in 10 - 15 working days

Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory. Methods of algebraic K-theory are actively used in algebra and related fields, achieving interesting results. This book presents the elements of algebraic K-theory, based essentially on the fundamental works of Milnor, Swan, Bass, Quillen, Karoubi, Gersten, Loday and Waldhausen. It includes all principal algebraic K-theories, connections with topological K-theory and cyclic homology, applications to the theory of monoid and polynomial algebras and in the theory of normed algebras. This volume will be of interest to graduate students and research mathematicians who want to learn more about K-theory.

Geometric Aspects of Probability Theory and Mathematical Statistics (Paperback, Softcover reprint of hardcover 1st ed. 2000):... Geometric Aspects of Probability Theory and Mathematical Statistics (Paperback, Softcover reprint of hardcover 1st ed. 2000)
V.V. Buldygin, A.B. Kharazishvili
R2,938 Discovery Miles 29 380 Ships in 10 - 15 working days

It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others."

Smooth Four-Manifolds and Complex Surfaces (Paperback, Softcover reprint of hardcover 1st ed. 1994): Robert Friedman, John W.... Smooth Four-Manifolds and Complex Surfaces (Paperback, Softcover reprint of hardcover 1st ed. 1994)
Robert Friedman, John W. Morgan
R5,647 Discovery Miles 56 470 Ships in 10 - 15 working days

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.

Diophantine Approximation on Linear Algebraic Groups - Transcendence Properties of the Exponential Function in Several... Diophantine Approximation on Linear Algebraic Groups - Transcendence Properties of the Exponential Function in Several Variables (Paperback, Softcover reprint of hardcover 1st ed. 2000)
Michel Waldschmidt
R2,981 Discovery Miles 29 810 Ships in 10 - 15 working days

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

Many Rational Points - Coding Theory and Algebraic Geometry (Paperback, 1st ed. Softcover of orig. ed. 2004): N. E. Hurt Many Rational Points - Coding Theory and Algebraic Geometry (Paperback, 1st ed. Softcover of orig. ed. 2004)
N. E. Hurt
R2,894 Discovery Miles 28 940 Ships in 10 - 15 working days

2 Triangle Groups: An Introduction 279 3 Elementary Shimura Curves 281 4 Examples of Shimura Curves 282 5 Congruence Zeta Functions 283 6 Diophantine Properties of Shimura Curves 284 7 Klein Quartic 285 8 Supersingular Points 289 Towers of Elkies 9 289 7. CRYPTOGRAPHY AND APPLICATIONS 291 1 Introduction 291 Discrete Logarithm Problem 2 291 Curves for Public-Key Cryptosystems 3 295 Hyperelliptic Curve Cryptosystems 4 297 CM-Method 5 299 6 Cryptographic Exponent 300 7 Constructive Descent 302 8 Gaudry and Harley Algorithm 306 9 Picard Jacobians 307 Drinfeld Module Based Public Key Cryptosystems 10 308 11 Drinfeld Modules and One Way Functions 308 12 Shimura's Map 309 13 Modular Jacobians of Genus 2 Curves 310 Modular Jacobian Surfaces 14 312 15 Modular Curves of Genus Two 313 16 Hecke Operators 314 8. REFERENCES 317 345 Index Xll Preface The history of counting points on curves over finite fields is very ex- tensive, starting with the work of Gauss in 1801 and continuing with the work of Artin, Schmidt, Hasse and Weil in their study of curves and the related zeta functions Zx(t), where m Zx(t) = exp (2: N t ) m m 2': 1 m with N = #X(F qm). If X is a curve of genus g, Weil's conjectures m state that L(t) Zx(t) = (1 - t)(l - qt) where L(t) = rr~!l (1 - O'.

Algebraic Model Theory (Paperback, Softcover reprint of hardcover 1st ed. 1997): Bradd T. Hart, A. Lachlan, Matthew A. Valeriote Algebraic Model Theory (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Bradd T. Hart, A. Lachlan, Matthew A. Valeriote
R4,349 Discovery Miles 43 490 Ships in 10 - 15 working days

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Fixed Point Theory and Best Approximation: The KKM-map Principle (Paperback, Softcover reprint of the original 1st ed. 1997):... Fixed Point Theory and Best Approximation: The KKM-map Principle (Paperback, Softcover reprint of the original 1st ed. 1997)
S.P. Singh, B Watson, P Srivastava
R2,873 Discovery Miles 28 730 Ships in 10 - 15 working days

The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before. Here, several topics of current and growing interest are systematically presented, such as fixed point theory, best approximation, the KKM-map principle, and results related to optimization theory, variational inequalities and complementarity problems. Illustrations of suitable applications are given, the links between results in various fields of research are highlighted, and an up-to-date bibliography is included to assist readers in further studies. Audience: This book will be of interest to graduate students, researchers and applied mathematicians working in nonlinear functional analysis, operator theory, approximations and expansions, convex sets and related geometric topics and game theory.

Riemann-Roch Algebra (Paperback, Softcover reprint of hardcover 1st ed. 1985): William Fulton, Serge Lang Riemann-Roch Algebra (Paperback, Softcover reprint of hardcover 1st ed. 1985)
William Fulton, Serge Lang
R3,119 Discovery Miles 31 190 Ships in 10 - 15 working days

In various contexts of topology, algebraic geometry, and algebra (e.g. group representations), one meets the following situation. One has two contravariant functors K and A from a certain category to the category of rings, and a natural transformation p: K--+A of contravariant functors. The Chern character being the central exam ple, we call the homomorphisms Px: K(X)--+ A(X) characters. Given f: X--+ Y, we denote the pull-back homomorphisms by and fA: A(Y)--+ A(X). As functors to abelian groups, K and A may also be covariant, with push-forward homomorphisms and fA: A( X)--+ A(Y). Usually these maps do not commute with the character, but there is an element r f E A(X) such that the following diagram is commutative: K(X) A(X) fK j J A K( Y) ------p;-+ A( Y) The map in the top line is p x multiplied by r f. When such commutativity holds, we say that Riemann-Roch holds for f. This type of formulation was first given by Grothendieck, extending the work of Hirzebruch to such a relative, functorial setting. Since then viii INTRODUCTION several other theorems of this Riemann-Roch type have appeared. Un derlying most of these there is a basic structure having to do only with elementary algebra, independent of the geometry. One purpose of this monograph is to describe this algebra independently of any context, so that it can serve axiomatically as the need arises."

Continuous Selections of Multivalued Mappings (Paperback, Softcover reprint of hardcover 1st ed. 1998): D. Repovs, P.V. Semenov Continuous Selections of Multivalued Mappings (Paperback, Softcover reprint of hardcover 1st ed. 1998)
D. Repovs, P.V. Semenov
R4,371 Discovery Miles 43 710 Ships in 10 - 15 working days

This book is dedicated to the theory of continuous selections of multi valued mappings, a classical area of mathematics (as far as the formulation of its fundamental problems and methods of solutions are concerned) as well as 'J-n area which has been intensively developing in recent decades and has found various applications in general topology, theory of absolute retracts and infinite-dimensional manifolds, geometric topology, fixed-point theory, functional and convex analysis, game theory, mathematical economics, and other branches of modern mathematics. The fundamental results in this the ory were laid down in the mid 1950's by E. Michael. The book consists of (relatively independent) three parts - Part A: Theory, Part B: Results, and Part C: Applications. (We shall refer to these parts simply by their names). The target audience for the first part are students of mathematics (in their senior year or in their first year of graduate school) who wish to get familiar with the foundations of this theory. The goal of the second part is to give a comprehensive survey of the existing results on continuous selections of multivalued mappings. It is intended for specialists in this area as well as for those who have mastered the material of the first part of the book. In the third part we present important examples of applications of continuous selections. We have chosen examples which are sufficiently interesting and have played in some sense key role in the corresponding areas of mathematics."

The Steiner Ratio (Paperback, Softcover reprint of hardcover 1st ed. 2001): Dietmar Cieslik The Steiner Ratio (Paperback, Softcover reprint of hardcover 1st ed. 2001)
Dietmar Cieslik
R2,911 Discovery Miles 29 110 Ships in 10 - 15 working days

Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms.

Theory of Commuting Nonselfadjoint Operators (Paperback, Softcover reprint of hardcover 1st ed. 1995): M.S Livsic, N.... Theory of Commuting Nonselfadjoint Operators (Paperback, Softcover reprint of hardcover 1st ed. 1995)
M.S Livsic, N. Kravitsky, A. S Markus, V. Vinnikov
R4,362 Discovery Miles 43 620 Ships in 10 - 15 working days

Considering integral transformations of Volterra type, F. Riesz and B. Sz.-Nagy no ticed in 1952 that [49]: "The existence of such a variety of linear transformations, having the same spectrum concentrated at a single point, brings out the difficulties of characterization of linear transformations of general type by means of their spectra." Subsequently, spectral analysis has been developed for different classes of non selfadjoint operators [6,7,14,20,21,36,44,46,54]. It was then realized that this analysis forms a natural basis for the theory of systems interacting with the environment. The success of this theory in the single operator case inspired attempts to create a general theory in the much more complicated case of several commuting operators with finite-dimensional imaginary parts. During the past 10-15 years such a theory has been developed, yielding fruitful connections with algebraic geometry and sys tem theory. Our purpose in this book is to formulate the basic problems appearing in this theory and to present its main results. It is worth noting that, in addition to the joint spectrum, the corresponding algebraic variety and its global topological characteristics play an important role in the classification of commuting operators. For the case of a pair of operators these are: 1. The corresponding algebraic curve, and especially its genus. 2. Certain classes of divisors - or certain line bundles - on this curve.

Resolution of Singularities of Embedded Algebraic Surfaces (Paperback, Softcover reprint of hardcover 2nd ed. 1998): Shreeram... Resolution of Singularities of Embedded Algebraic Surfaces (Paperback, Softcover reprint of hardcover 2nd ed. 1998)
Shreeram S. Abhyankar
R2,882 Discovery Miles 28 820 Ships in 10 - 15 working days

The common solutions of a finite number of polynomial equations in a finite number of variables constitute an algebraic variety. The degrees of freedom of a moving point on the variety is the dimension of the variety. A one-dimensional variety is a curve and a two-dimensional variety is a surface. A three-dimensional variety may be called asolid. Most points of a variety are simple points. Singularities are special points, or points of multiplicity greater than one. Points of multiplicity two are double points, points of multiplicity three are tripie points, and so on. A nodal point of a curve is a double point where the curve crosses itself, such as the alpha curve. A cusp is a double point where the curve has a beak. The vertex of a cone provides an example of a surface singularity. A reversible change of variables gives abirational transformation of a variety. Singularities of a variety may be resolved by birational transformations.

Non-Abelian Homological Algebra and Its Applications (Paperback, Softcover reprint of hardcover 1st ed. 1997): Hvedri... Non-Abelian Homological Algebra and Its Applications (Paperback, Softcover reprint of hardcover 1st ed. 1997)
Hvedri Inassaridze
R4,348 Discovery Miles 43 480 Ships in 10 - 15 working days

While in classical (abelian) homological algebra additive functors from abelian (or additive) categories to abelian categories are investigated , non- abelian homological algebra deals with non-additive functors and their homological properties , in particular with functors having values in non-abelian categories. Such functors haveimportant applications in algebra, algebraic topology, functional analysis, algebraic geometry and other principal areas of mathematics. To study homological properties of non-additive functors it is necessary to define and investigate their derived functors and satellites. It will be the aim of this book based on the results of researchers of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences devoted to non-abelian homological algebra. The most important considered cases will be functors from arbitrary categories to the category of modules, group valued functors and commutative semigroup valued functors. In Chapter I universal sequences of functors are defined and in- vestigated with respect to (co)presheaves of categories, extending in a natural way the satellites of additive functors to the non-additive case and generalizing the classical relative homological algebra in additive categories to arbitrary categories. Applications are given in the furth- coming chapters. Chapter II is devoted to the non-abelian derived functors of group valued functors with respect to projective classes using projective pseu- dosimplicial resolutions. Their functorial properties (exactness, Milnor exact sequence, relationship with cotriple derived functors, satellites and Grothendieck cohomology, spectral sequence of an epimorphism, degree of an arbitrary functor) are established and applications to ho- mology and cohomology of groups are given.

Resolution of Curve and Surface Singularities in Characteristic Zero (Paperback, Softcover reprint of hardcover 1st ed. 2004):... Resolution of Curve and Surface Singularities in Characteristic Zero (Paperback, Softcover reprint of hardcover 1st ed. 2004)
K. Kiyek, J.L. Vicente
R1,584 Discovery Miles 15 840 Ships in 10 - 15 working days

The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. ** . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it * To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.

Coding Theory and Number Theory (Paperback, Softcover reprint of hardcover 1st ed. 2003): T. Hiramatsu, Gunter Koehler Coding Theory and Number Theory (Paperback, Softcover reprint of hardcover 1st ed. 2003)
T. Hiramatsu, Gunter Koehler
R1,490 Discovery Miles 14 900 Ships in 10 - 15 working days

This book grew out of our lectures given in the Oberseminar on 'Cod ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding the ory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the math ematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chap ter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over fi nite fields and the theory of q-ary codes."

Meromorphic Functions and Projective Curves (Paperback, Softcover reprint of hardcover 1st ed. 1999): Kichoon Yang Meromorphic Functions and Projective Curves (Paperback, Softcover reprint of hardcover 1st ed. 1999)
Kichoon Yang
R2,873 Discovery Miles 28 730 Ships in 10 - 15 working days

This book contains an exposition of the theory of meromorphic functions and linear series on a compact Riemann surface. Thus the main subject matter consists of holomorphic maps from a compact Riemann surface to complex projective space. Our emphasis is on families of meromorphic functions and holomorphic curves. Our approach is more geometric than algebraic along the lines of [Griffiths-Harrisl]. AIso, we have relied on the books [Namba] and [Arbarello-Cornalba-Griffiths-Harris] to agreat exten- nearly every result in Chapters 1 through 4 can be found in the union of these two books. Our primary motivation was to understand the totality of meromorphic functions on an algebraic curve. Though this is a classical subject and much is known about meromorphic functions, we felt that an accessible exposition was lacking in the current literature. Thus our book can be thought of as a modest effort to expose parts of the known theory of meromorphic functions and holomorphic curves with a geometric bent. We have tried to make the book self-contained and concise which meant that several major proofs not essential to further development of the theory had to be omitted. The book is targeted at the non-expert who wishes to leam enough about meromorphic functions and holomorphic curves so that helshe will be able to apply the results in hislher own research. For example, a differential geometer working in minimal surface theory may want to tind out more about the distribution pattern of poles and zeros of a meromorphic function.

Algebraic Cobordism (Paperback, 1st ed. Softcover of orig. ed. 2007): Marc Levine, Fabien Morel Algebraic Cobordism (Paperback, 1st ed. Softcover of orig. ed. 2007)
Marc Levine, Fabien Morel
R2,863 Discovery Miles 28 630 Ships in 10 - 15 working days

Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. The book also contains some examples of computations and applications.

Simplicial Methods for Operads and Algebraic Geometry (Paperback, 2010 ed.): Ieke Moerdijk, Bertrand Toen Simplicial Methods for Operads and Algebraic Geometry (Paperback, 2010 ed.)
Ieke Moerdijk, Bertrand Toen
R1,029 Discovery Miles 10 290 Ships in 10 - 15 working days

This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures - livered at the Centre de Recerca Matem ati ca in February 2008, as part of a special year on Homotopy Theory and Higher Categories. Ieke Moerdijk's lectures constitute an introduction to the theory ofdendroidal sets, an extension of the theory of simplicial sets designed as a foundation for the homotopy theory of operads. The theory has many features analogous to the theory of simplicial sets, but it also reveals many new phenomena, thanks to the presence of automorphisms of trees. Dendroidal sets admit a closed symmetric monoidal structure related to the Boardman{Vogt tensor product. The lecture notes develop the theory very carefully, starting from scratch with the combinatorics of trees, and culminating with a model structure on the category of dendroidal sets for which the brant objects are the inner Kan dendroidal sets. The important concepts are illustrated with detailed examples.

Rational Points on Elliptic Curves (Paperback, Softcover reprint of hardcover 1st ed. 1992): Joseph H. Silverman, John Tate Rational Points on Elliptic Curves (Paperback, Softcover reprint of hardcover 1st ed. 1992)
Joseph H. Silverman, John Tate
R1,277 Discovery Miles 12 770 Ships in 10 - 15 working days

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book 's accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

Neron Models (Paperback, Softcover reprint of the original 1st ed. 1990): Siegfried Bosch, Werner L utkebohmert, Michel Raynaud Neron Models (Paperback, Softcover reprint of the original 1st ed. 1990)
Siegfried Bosch, Werner L utkebohmert, Michel Raynaud
R5,127 Discovery Miles 51 270 Ships in 10 - 15 working days

Neron models were invented by A. Neron in the early 1960s in order to study the integral structure of abelian varieties over number fields. Since then, arithmeticians and algebraic geometers have applied the theory of Neron models with great success. Quite recently, new developments in arithmetic algebraic geometry have prompted a desire to understand more about Neron models, and even to go back to the basics of their construction. The authors have taken this as their incentive to present a comprehensive treatment of Neron models. This volume of the renowned "Ergebnisse" series provides a detailed demonstration of the construction of Neron models from the point of view of Grothendieck's algebraic geometry. In the second part of the book the relationship between Neron models and the relative Picard functor in the case of Jacobian varieties is explained. The authors helpfully remind the reader of some important standard techniques of algebraic geometry. A special chapter surveys the theory of the Picard functor.

Algebra IX - Finite Groups of Lie Type Finite-Dimensional Division Algebras (Paperback, Softcover reprint of the original 1st... Algebra IX - Finite Groups of Lie Type Finite-Dimensional Division Algebras (Paperback, Softcover reprint of the original 1st ed. 1996)
R.W. Carter; Translated by P. M. Cohn; Edited by A.I. Kostrikin, I.R. Shafarevich; Contributions by V.P. Platonov, …
R2,873 Discovery Miles 28 730 Ships in 10 - 15 working days

The first contribution by Carter covers the theory of finite groups of Lie type, an important field of current mathematical research. In the second part, Platonov and Yanchevskii survey the structure of finite-dimensional division algebras, including an account of reduced K-theory.

Geometry of Algebraic Curves - Volume I (Paperback, 1985 ed.): Enrico Arbarello, Maurizio Cornalba, Phillip Griffiths, Joseph... Geometry of Algebraic Curves - Volume I (Paperback, 1985 ed.)
Enrico Arbarello, Maurizio Cornalba, Phillip Griffiths, Joseph Daniel Harris
R2,660 Discovery Miles 26 600 Ships in 10 - 15 working days

In recent years there has been enormous activity in the theory of algebraic curves. Many long-standing problems have been solved using the general techniques developed in algebraic geometry during the 1950's and 1960's. Additionally, unexpected and deep connections between algebraic curves and differential equations have been uncovered, and these in turn shed light on other classical problems in curve theory. It seems fair to say that the theory of algebraic curves looks completely different now from how it appeared 15 years ago; in particular, our current state of knowledge repre sents a significant advance beyond the legacy left by the classical geometers such as Noether, Castelnuovo, Enriques, and Severi. These books give a presentation of one of the central areas of this recent activity; namely, the study of linear series on both a fixed curve (Volume I) and on a variable curve (Volume II). Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory. Along the way we shall, of course, discuss appli cations of the theory of linear series to a number of classical topics (e.g., the geometry of the Riemann theta divisor) as well as to some of the current research (e.g., the Kodaira dimension of the moduli space of curves)."

Algebraic Geometry - A First Course (Paperback, Softcover reprint of hardcover 1st ed. 1992): Joe Harris Algebraic Geometry - A First Course (Paperback, Softcover reprint of hardcover 1st ed. 1992)
Joe Harris
R1,907 Discovery Miles 19 070 Ships in 10 - 15 working days

"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

Geometric Inequalities (Paperback, Softcover reprint of the original 1st ed. 1988): Yurii D. Burago Geometric Inequalities (Paperback, Softcover reprint of the original 1st ed. 1988)
Yurii D. Burago; Translated by A.B. Sossinsky; Viktor A. Zalgaller
R4,365 Discovery Miles 43 650 Ships in 10 - 15 working days

Geometrie inequalities have a wide range of applieations-within geometry itself as weIl as beyond its limits. The theory of funetions of a eomplex variable, the ealculus of variations in the large, embedding theorems of funetion spaees, a priori estimates for solutions of differential equations yield many sueh examples. We have attempted to piek out the most general inequalities and, in model eases, we exhibit effeetive geometrie eonstruetions and the means of proving sueh inequalities. A substantial part of this book deals with isoperimetrie inequalities and their generalizations, but, for all their variety, they do not exhaust the eontents ofthe book. The objeets under eonsideration, as a rule, are quite general. They are eurves, surfaees and other manifolds, embedded in an underlying space or supplied with an intrinsie metrie. Geometrie inequalities, used for different purposes, appear in different eontexts-surrounded by a variety ofteehnieal maehinery, with diverse require- ments for the objeets under study. Therefore the methods of proof will differ not only from ehapter to ehapter, but even within individual seetions. An inspeetion of monographs on algebraie and funetional inequalities ([HLP], [BeB], [MV], [MM]) shows that this is typical for books of this type.

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