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

Algorithmic Algebra and Number Theory - Selected Papers From a Conference Held at the University of Heidelberg in October 1997... Algorithmic Algebra and Number Theory - Selected Papers From a Conference Held at the University of Heidelberg in October 1997 (Paperback, Softcover reprint of the original 1st ed. 1999)
B. Heinrich Matzat, Gert-Martin Greuel, Gerhard Hiss
R2,918 Discovery Miles 29 180 Ships in 10 - 15 working days

This book contains 22 lectures presented at the final conference of the Ger man research program (Schwerpunktprogramm) Algorithmic Number The ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com putational methods to gain insight into experimental problems and theoret ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob tained during this period. This includes survey articles on the main research projects within the program: * algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules * computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups * computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer algebra sys tems and program packages developed with support by the research pro gram, such as KANT and LiDIA for algebraic number theory, SINGULAR, RED LOG and INVAR for commutative algebra and invariant theory respec tively, and GAP, SYSYPHOS and CHEVIE for group theory and representation theory.

Algebraic Geometry I - Algebraic Curves, Algebraic Manifolds and Schemes (Paperback, Softcover reprint of the original 1st ed.... Algebraic Geometry I - Algebraic Curves, Algebraic Manifolds and Schemes (Paperback, Softcover reprint of the original 1st ed. 1994)
V.I. Danilov; Edited by I. Shafarevich; Translated by D. Coray, V.N. Shokurov; V.V. Shokurov
R5,095 Discovery Miles 50 950 Ships in 10 - 15 working days

From the reviews: "This volume... consists of two papers. The first, written by V.V. Shokurov, is devoted to the theory of Riemann surfaces and algebraic curves. It is an excellent overview of the theory of relations between Riemann surfaces and their models - complex algebraic curves in complex projective spaces. ... The second paper, written by V.I. Danilov, discusses algebraic varieties and schemes. ... I can recommend the book as a very good introduction to the basic algebraic geometry." "European Mathematical Society" "Newsletter, 1996"
..". To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." Acta Scientiarum Mathematicarum

Moduli of Supersingular Abelian Varieties (Paperback, 1998 ed.): Ke-Zheng Li, Frans Oort Moduli of Supersingular Abelian Varieties (Paperback, 1998 ed.)
Ke-Zheng Li, Frans Oort
R1,128 Discovery Miles 11 280 Ships in 10 - 15 working days

Abelian varieties can be classified via their moduli. In positive characteristic the structure of the p-torsion-structure is an additional, useful tool. For that structure supersingular abelian varieties can be considered the most special ones. They provide a starting point for the fine description of various structures. For low dimensions the moduli of supersingular abelian varieties is by now well understood. In this book we provide a description of the supersingular locus in all dimensions, in particular we compute the dimension of it: it turns out to be equal to AEg.g/4UE, and we express the number of components as a class number, thus completing a long historical line where special cases were studied and general results were conjectured (Deuring, Hasse, Igusa, Oda-Oort, Katsura-Oort).

Intersection Theory (Paperback, 2nd ed. 1998): William Fulton Intersection Theory (Paperback, 2nd ed. 1998)
William Fulton
R3,571 Discovery Miles 35 710 Ships in 10 - 15 working days

From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the foundations of this theory, and to indicate the range of classical and modern applications. Although a comprehensive history of this vast subject is not attempted, the author points out some of the striking early appearances of the ideas of intersection theory. A suggested prerequisite for the reading of this book is a first course in algebraic geometry. Fulton's introduction to intersection theory has been well used for more than 10 years. It is still the only existing complete modern treatise of the subject and received the Steele Prize for best exposition in August 1996.

Algebraic Homogeneous Spaces and Invariant Theory (Paperback): Frank D. Grosshans Algebraic Homogeneous Spaces and Invariant Theory (Paperback)
Frank D. Grosshans
R1,411 Discovery Miles 14 110 Ships in 10 - 15 working days

The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.

Number Theory III - Diophantine Geometry (Paperback, Softcover reprint of the original 1st ed. 1991): Serge Lang Number Theory III - Diophantine Geometry (Paperback, Softcover reprint of the original 1st ed. 1991)
Serge Lang; Serge Lang
R2,977 Discovery Miles 29 770 Ships in 10 - 15 working days

In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideas for the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more."

Realizations of Polylogarithms (Paperback, 1997 ed.): Joerg Wildeshaus Realizations of Polylogarithms (Paperback, 1997 ed.)
Joerg Wildeshaus
R1,648 Discovery Miles 16 480 Ships in 10 - 15 working days

Classically, higher logarithms appear as multivalued functions on the projective line. Today they can be interpreted as entries of the period matrix of a certain variation of Hodge structure, itself called the "polylogarithm." The aim of the book is to document the sheaf-theoretical foundations of the field of polylogarithms. Earlier, partly unpublished results and constructions of Beilinson, Deligne, and Levin on the classical and elliptic polylog are generalized to the context of Shimura varieties. The reader is expected to have a sound background in algebraic geometry. Large parts of the book are expository, and intended as a reference for the working mathematician. Where a self-contained exposition was not possible, the author gives references in order to make the material accessible for advanced graduate students.

Geometry of Higher Dimensional Algebraic Varieties (Paperback, 1997 ed.): Thomas Peternell, Joichi Miyaoka Geometry of Higher Dimensional Algebraic Varieties (Paperback, 1997 ed.)
Thomas Peternell, Joichi Miyaoka
R1,469 Discovery Miles 14 690 Ships in 10 - 15 working days

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory." The construction of minimal models was discussed by T."

Lie Groups and Lie Algebras I - Foundations of Lie Theory Lie Transformation Groups (Paperback, Softcover reprint of the... Lie Groups and Lie Algebras I - Foundations of Lie Theory Lie Transformation Groups (Paperback, Softcover reprint of the original 1st ed. 1993)
V.V. Gorbatsevich; Edited by A.L. Onishchik; Translated by T. Kozlowski; A.L. Onishchik, E.B. Vinberg
R2,938 Discovery Miles 29 380 Ships in 10 - 15 working days

From the reviews:
.."., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?"
"The New Zealand Mathematical Society Newsletter"
..". Both parts are very nicely written and can be strongly recommended."
"European Mathematical Society"

Configuration Spaces over Hilbert Schemes and Applications (Paperback, 1996 ed.): Danielle Dias, Patrick Le Barz Configuration Spaces over Hilbert Schemes and Applications (Paperback, 1996 ed.)
Danielle Dias, Patrick Le Barz
R1,163 Discovery Miles 11 630 Ships in 10 - 15 working days

The main themes of this book are to establish the triple formula without any hypotheses on the genericity of the morphism, and to develop a theory of complete quadruple points, which is a first step towards proving the quadruple point formula under less restrictive hypotheses.
This book should be of interest to graduate students and researchers in the field of algebraic geometry. The reader is expected to have some basic knowledge of enumerative algebraic geometry and pointwise Hilbert schemes.

Transcendental Methods in Algebraic Geometry - Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo... Transcendental Methods in Algebraic Geometry - Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in Cetraro, Italy, July 4-12, 1994 (Paperback, 1996 ed.)
Fabrizio Catanese; Jean-Pierre Demailly; Edited by Ciro Ciliberto; Thomas Peternell, Gang Tian, …
R1,601 Discovery Miles 16 010 Ships in 10 - 15 working days
Moduli of Abelian Varieties (Paperback, 1996 ed.): Allan Adler, Sundararaman Ramanan Moduli of Abelian Varieties (Paperback, 1996 ed.)
Allan Adler, Sundararaman Ramanan
R1,440 Discovery Miles 14 400 Ships in 10 - 15 working days

This is a book aimed at researchers and advanced graduate students in algebraic geometry, interested in learning about a promising direction of research in algebraic geometry. It begins with a generalization of parts of Mumford's theory of the equations defining abelian varieties and moduli spaces. It shows through striking examples how one can use these apparently intractable systems of equations to obtain satisfying insights into the geometry and arithmetic of these varieties. It also introduces the reader to some aspects of the research of the first author into representation theory and invariant theory and their applications to these geometrical questions.

The semi-simple zeta function of quaternionic Shimura varieties (Paperback, 1997 ed.): Harry Reimann The semi-simple zeta function of quaternionic Shimura varieties (Paperback, 1997 ed.)
Harry Reimann
R1,414 Discovery Miles 14 140 Ships in 10 - 15 working days

This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.

Realization Spaces of Polytopes (Paperback, 1996 ed.): Jurgen Richter-Gebert Realization Spaces of Polytopes (Paperback, 1996 ed.)
Jurgen Richter-Gebert
R1,436 Discovery Miles 14 360 Ships in 10 - 15 working days

The book collects results about realization spaces of polytopes. It gives a presentation of the author's "Universality Theorem for 4-polytopes." It is a comprehensive survey of the important results that have been obtained in that direction. The approaches chosen are direct and very geometric in nature. The book is addressed to researchers and to graduate students. The former will find a comprehensive source for the above mentioned results. The latter will find a readable introduction to the field. The reader is assumed to be familiar with basic concepts of linear algebra.

Topics in Cohomology of Groups (Paperback, 1996 ed.): Serge Lang Topics in Cohomology of Groups (Paperback, 1996 ed.)
Serge Lang
R1,703 Discovery Miles 17 030 Ships in 10 - 15 working days

The book is a mostly translated reprint of a report on cohomology of groups from the 1950s and 1960s, originally written as background for the Artin-Tate notes on class field theory, following the cohomological approach. This report was first published (in French) by Benjamin. For this new English edition, the author added Tate's local duality, written up from letters which John Tate sent to Lang in 1958 - 1959. Except for this last item, which requires more substantial background in algebraic geometry and especially abelian varieties, the rest of the book is basically elementary, depending only on standard homological algebra at the level of first year graduate students.

The Geometry of some special Arithmetic Quotients (Paperback, 1996 ed.): Bruce Hunt The Geometry of some special Arithmetic Quotients (Paperback, 1996 ed.)
Bruce Hunt
R1,771 Discovery Miles 17 710 Ships in 10 - 15 working days

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest to all involved in the study of moduli spaces with symmetries, and contains in addition a wealth of material which has been only accessible in very old sources, including a detailed presentation of the solution of the equation of 27th degree for the lines on a cubic surface.

Spaces of Orderings and Abstract Real Spectra (Paperback, 1996 ed.): Murray a Marshall Spaces of Orderings and Abstract Real Spectra (Paperback, 1996 ed.)
Murray a Marshall
R1,436 Discovery Miles 14 360 Ships in 10 - 15 working days

This book is of interest to students as well as experts in the area of real algebraic geometry, quadratic forms, orderings, valuations, lattice ordered groups and rings, and in model theory. The original motivation comes from orderings on fields and commutative rings. This is explained as is the important application to minimal generation of semi-algebraic sets. Many results in the new theory of abstract real spectra (also called spaces of signs) appear here for the first time. The reader needs elementary knowledge of commutative rings, ordered fields and real closed fields and valuations.

Integrable Systems and Quantum Groups - Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo... Integrable Systems and Quantum Groups - Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1993 (Paperback, 1996 ed.)
Ron Donagi; Edited by Mauro Francaviglia, Silvio Greco; Boris Dubrovin, Edward Frenkel, …
R2,348 Discovery Miles 23 480 Ships in 10 - 15 working days

The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields. The papers contained in this volume have at the same time the character of survey articles and of research papers, since they contain both a survey of current problems and a number of original contributions to the subject.

A Compactification of the Bruhat-Tits Building (Paperback, 1996 ed.): Erasmus Landvogt A Compactification of the Bruhat-Tits Building (Paperback, 1996 ed.)
Erasmus Landvogt
R1,415 Discovery Miles 14 150 Ships in 10 - 15 working days

The aim of this work is the definition of the polyhedral compactification of the Bruhat-Tits building of a reductive group over a local field. In addition, an explicit description of the boundary is given. In order to make this work as self-contained as possible and also accessible to non-experts in Bruhat-Tits theory, the construction of the Bruhat-Tits building itself is given completely.

Mixed Motives and their Realization in Derived Categories (Paperback, 1995 ed.): Annette Huber Mixed Motives and their Realization in Derived Categories (Paperback, 1995 ed.)
Annette Huber
R1,576 Discovery Miles 15 760 Ships in 10 - 15 working days

The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives via their well-defined realizations. This includes a review of several known cohomology theories. A new absolute cohomology is introduced and studied.
The book assumes knowledge of the standard cohomological techniques in algebraic geometry as well as K-theory. So the monograph is primarily intended for researchers. Advanced graduate students can use it as a guide to the literature.

The Classification of Three-dimensional Homogeneous Complex Manifolds (Paperback, 1995 ed.): Joerg Winkelmann The Classification of Three-dimensional Homogeneous Complex Manifolds (Paperback, 1995 ed.)
Joerg Winkelmann
R1,954 Discovery Miles 19 540 Ships in 10 - 15 working days

This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group. This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. The classification is based on methods from Lie group theory, complex analysis and algebraic geometry. Basic knowledge in these areas is presupposed.

Topological Methods in Algebraic Geometry - Reprint of the 1978 Edition (Paperback, Reprint of the 1st ed): Friedrich Hirzebruch Topological Methods in Algebraic Geometry - Reprint of the 1978 Edition (Paperback, Reprint of the 1st ed)
Friedrich Hirzebruch; Translated by R. L. E. Schwarzenberger; Appendix by R. L. E. Schwarzenberger, A Borel
R1,647 Discovery Miles 16 470 Ships in 10 - 15 working days

In recent years new topological methods, especially the theory of sheaves founded by J. LERAY, have been applied successfully to algebraic geometry and to the theory of functions of several complex variables. H. CARTAN and J. -P. SERRE have shown how fundamental theorems on holomorphically complete manifolds (STEIN manifolds) can be for mulated in terms of sheaf theory. These theorems imply many facts of function theory because the domains of holomorphy are holomorphically complete. They can also be applied to algebraic geometry because the complement of a hyperplane section of an algebraic manifold is holo morphically complete. J. -P. SERRE has obtained important results on algebraic manifolds by these and other methods. Recently many of his results have been proved for algebraic varieties defined over a field of arbitrary characteristic. K. KODAIRA and D. C. SPENCER have also applied sheaf theory to algebraic geometry with great success. Their methods differ from those of SERRE in that they use techniques from differential geometry (harmonic integrals etc. ) but do not make any use of the theory of STEIN manifolds. M. F. ATIYAH and W. V. D. HODGE have dealt successfully with problems on integrals of the second kind on algebraic manifolds with the help of sheaf theory. I was able to work together with K. KODAIRA and D. C. SPENCER during a stay at the Institute for Advanced Study at Princeton from 1952 to 1954."

The Ball and Some Hilbert Problems (Paperback, 1995 ed.): Rolf-Peter Holzapfel The Ball and Some Hilbert Problems (Paperback, 1995 ed.)
Rolf-Peter Holzapfel
R1,497 Discovery Miles 14 970 Ships in 10 - 15 working days

As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 prob lems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field." This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S pro gram. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21."

Contributions to Complex Analysis and Analytic Geometry - Dedicated to P.Dolbeault (Paperback, 1994 Ed.): Henri Skoda,... Contributions to Complex Analysis and Analytic Geometry - Dedicated to P.Dolbeault (Paperback, 1994 Ed.)
Henri Skoda, Jean-Marie Trepreau
R1,630 Discovery Miles 16 300 Ships in 10 - 15 working days

Preface of the Editors Ce volume prend sa source dans le Colloque en l'honneur de Pierre Dolbeault, organise a l'occasion de son depart a la retraite, a 'initiative des Universites de Paris 6 et de Poitiers. Ce colloque, consacre a l' Analyse Complexe et a la Geometrie Analytique, s'est tenu a Paris, sur le campus de l'Universite Pierreet Marie Curie, du 23 au 26 Juin 1992.11 areuni autour de ces themes une centaine de congressistes, dont de nombreux mathematiciens etrangers (Allemagne, Argentine, Canada, Etats-Unis, Islande, Italie, Pologne, Roumanie, Russie, Suede). Nous avons souhaite prolanger cet hommage par la publication d'un volume dedie a Pierre Dolbeault. Le present recueil d'articles ne constitue pas strictement les actes du Colloque. Nous avons voulu qu'il rassemble uniquement des articles originaux ou synthetiques, qui illustrent l' ceuvre scientifique de Pierre Dolbeault a travers les themes abordes ou la personnalite de leurs auteurs. Nous remercions les conferenciers qui ont bien voulu contribuer a cet ouvrage, et Klas Diederich de l'avoir accueilli dans la collection "Aspects of Mathematics" qu'il dirige. Au nom du Comite d'Organisation du Colloque (C. Laurent-Thiebaut, J. Le Potier, J.B. Poly, J.P. Vigue et nous-memes), nous remercions les institutions qui nous ont apporte leur aide financiere et materielle: les Universites Paris 6 et de Poitiers, la Direction de la Recherche et des Etudes Doctorales, le Centre National de la Recherche Scientifique et le Ministere de la Recherche et de la Technologie.

Introduction to Etale Cohomology (Paperback, Softcover reprint of the original 1st ed. 1994): M. Kolster Introduction to Etale Cohomology (Paperback, Softcover reprint of the original 1st ed. 1994)
M. Kolster; G unter Tamme
R2,628 Discovery Miles 26 280 Ships in 10 - 15 working days

Etale Cohomology is one of the most important methods in modern Algebraic Geometry and Number Theory. It has, in the last decades, brought fundamental new insights in arithmetic and algebraic geometric problems with many applications and many important results. The book gives a short and easy introduction into the world of Abelian Categories, Derived Functors, Grothendieck Topologies, Sheaves, General Etale Cohomology, and Etale Cohomology of Curves."

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