|
Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry
This volume is a tribute to Maxim Kontsevich, one of the most
original and influential mathematicians of our time. Maxim's vision
has inspired major developments in many areas of mathematics,
ranging all the way from probability theory to motives over finite
fields, and has brought forth a paradigm shift at the interface of
modern geometry and mathematical physics. Many of his papers have
opened completely new directions of research and led to the
solutions of many classical problems. This book collects papers by
leading experts currently engaged in research on topics close to
Maxim's heart. Contributors: S. Donaldson A. Goncharov D. Kaledin
M. Kapranov A. Kapustin L. Katzarkov A. Noll P. Pandit S. Pimenov
J. Ren P. Seidel C. Simpson Y. Soibelman R. Thorngren
This volume contains selected papers authored by speakers and
participants of the 2013 Arbeitstagung, held at the Max Planck
Institute for Mathematics in Bonn, Germany, from May 22-28. The
2013 meeting (and this resulting proceedings) was dedicated to the
memory of Friedrich Hirzebruch, who passed away on May 27, 2012.
Hirzebruch organized the first Arbeitstagung in 1957 with a unique
concept that would become its most distinctive feature: the program
was not determined beforehand by the organizers, but during the
meeting by all participants in an open discussion. This ensured
that the talks would be on the latest developments in mathematics
and that many important results were presented at the conference
for the first time. Written by leading mathematicians, the papers
in this volume cover various topics from algebraic geometry,
topology, analysis, operator theory, and representation theory and
display the breadth and depth of pure mathematics that has always
been characteristic of the Arbeitstagung.
This book arose from a conference on "Singularities and Computer
Algebra" which was held at the Pfalz-Akademie Lambrecht in June
2015 in honor of Gert-Martin Greuel's 70th birthday. This unique
volume presents a collection of recent original research by some of
the leading figures in singularity theory on a broad range of
topics including topological and algebraic aspects, classification
problems, deformation theory and resolution of singularities. At
the same time, the articles highlight a variety of techniques,
ranging from theoretical methods to practical tools from computer
algebra.Greuel himself made major contributions to the development
of both singularity theory and computer algebra. With Gerhard
Pfister and Hans Schoenemann, he developed the computer algebra
system SINGULAR, which has since become the computational tool of
choice for many singularity theorists.The book addresses
researchers whose work involves singularity theory and computer
algebra from the PhD to expert level.
The purpose of this book is to present the classical analytic
function theory of several variables as a standard subject in a
course of mathematics after learning the elementary materials
(sets, general topology, algebra, one complex variable). This
includes the essential parts of Grauert-Remmert's two volumes,
GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic
sheaves) with a lowering of the level for novice graduate students
(here, Grauert's direct image theorem is limited to the case of
finite maps).The core of the theory is "Oka's Coherence", found and
proved by Kiyoshi Oka. It is indispensable, not only in the study
of complex analysis and complex geometry, but also in a large area
of modern mathematics. In this book, just after an introductory
chapter on holomorphic functions (Chap. 1), we prove Oka's First
Coherence Theorem for holomorphic functions in Chap. 2. This
defines a unique character of the book compared with other books on
this subject, in which the notion of coherence appears much
later.The present book, consisting of nine chapters, gives complete
treatments of the following items: Coherence of sheaves of
holomorphic functions (Chap. 2); Oka-Cartan's Fundamental Theorem
(Chap. 4); Coherence of ideal sheaves of complex analytic subsets
(Chap. 6); Coherence of the normalization sheaves of complex spaces
(Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's
Theorem for Riemann domains (Chap. 8). The theories of sheaf
cohomology and domains of holomorphy are also presented (Chaps. 3,
5). Chapter 6 deals with the theory of complex analytic subsets.
Chapter 8 is devoted to the applications of formerly obtained
results, proving Cartan-Serre's Theorem and Kodaira's Embedding
Theorem. In Chap. 9, we discuss the historical development of
"Coherence".It is difficult to find a book at this level that
treats all of the above subjects in a completely self-contained
manner. In the present volume, a number of classical proofs are
improved and simplified, so that the contents are easily accessible
for beginning graduate students.
This volume grew out of two Simons Symposia on "Nonarchimedean and
tropical geometry" which took place on the island of St. John in
April 2013 and in Puerto Rico in February 2015. Each meeting
gathered a small group of experts working near the interface
between tropical geometry and nonarchimedean analytic spaces for a
series of inspiring and provocative lectures on cutting edge
research, interspersed with lively discussions and collaborative
work in small groups. The articles collected here, which include
high-level surveys as well as original research, mirror the main
themes of the two Symposia. Topics covered in this volume include:
Differential forms and currents, and solutions of Monge-Ampere type
differential equations on Berkovich spaces and their skeletons; The
homotopy types of nonarchimedean analytifications; The existence of
"faithful tropicalizations" which encode the topology and geometry
of analytifications; Relations between nonarchimedean analytic
spaces and algebraic geometry, including logarithmic schemes,
birational geometry, and the geometry of algebraic curves; Extended
notions of tropical varieties which relate to Huber's theory of
adic spaces analogously to the way that usual tropical varieties
relate to Berkovich spaces; and Relations between nonarchimedean
geometry and combinatorics, including deep and fascinating
connections between matroid theory, tropical geometry, and Hodge
theory.
In the more than 100 years since the fundamental group was first
introduced by Henri Poincare it has evolved to play an important
role in different areas of mathematics. Originally conceived as
part of algebraic topology, this essential concept and its
analogies have found numerous applications in mathematics that are
still being investigated today, and which are explored in this
volume, the result of a meeting at Heidelberg University that
brought together mathematicians who use or study fundamental groups
in their work with an eye towards applications in arithmetic. The
book acknowledges the varied incarnations of the fundamental group:
pro-finite, -adic, p-adic, pro-algebraic and motivic. It explores a
wealth of topics that range from anabelian geometry (in particular
the section conjecture), the -adic polylogarithm, gonality
questions of modular curves, vector bundles in connection with
monodromy, and relative pro-algebraic completions, to a motivic
version of Minhyong Kim's non-abelian Chabauty method and p-adic
integration after Coleman. The editor has also included the
abstracts of all the talks given at the Heidelberg meeting, as well
as the notes on Coleman integration and on Grothendieck's
fundamental group with a view towards anabelian geometry taken from
a series of introductory lectures given by Amnon Besser and Tamas
Szamuely, respectively."
The book is devoted to the study of the geometrical and topological
structure of gauge theories. It consists of the following three
building blocks:- Geometry and topology of fibre bundles,- Clifford
algebras, spin structures and Dirac operators,- Gauge
theory.Written in the style of a mathematical textbook, it combines
a comprehensive presentation of the mathematical foundations with a
discussion of a variety of advanced topics in gauge theory.The
first building block includes a number of specific topics, like
invariant connections, universal connections, H-structures and the
Postnikov approximation of classifying spaces.Given the great
importance of Dirac operators in gauge theory, a complete proof of
the Atiyah-Singer Index Theorem is presented. The gauge theory part
contains the study of Yang-Mills equations (including the theory of
instantons and the classical stability analysis), the discussion of
various models with matter fields (including magnetic monopoles,
the Seiberg-Witten model and dimensional reduction) and the
investigation of the structure of the gauge orbit space. The final
chapter is devoted to elements of quantum gauge theory including
the discussion of the Gribov problem, anomalies and the
implementation of the non-generic gauge orbit strata in the
framework of Hamiltonian lattice gauge theory.The book is addressed
both to physicists and mathematicians. It is intended to be
accessible to students starting from a graduate level.
Featuring a blend of original research papers and comprehensive
surveys from an international team of leading researchers in the
thriving fields of foliation theory, holomorphic foliations, and
birational geometry, this book presents the proceedings of the
conference "Foliation Theory in Algebraic Geometry," hosted by the
Simons Foundation in New York City in September 2013. Topics
covered include: Fano and del Pezzo foliations; the cone theorem
and rank one foliations; the structure of symmetric differentials
on a smooth complex surface and a local structure theorem for
closed symmetric differentials of rank two; an overview of lifting
symmetric differentials from varieties with canonical singularities
and the applications to the classification of AT bundles on
singular varieties; an overview of the powerful theory of the
variety of minimal rational tangents introduced by Hwang and Mok;
recent examples of varieties which are hyperbolic and yet the
Green-Griffiths locus is the whole of X; and a classification of
psuedoeffective codimension one distributions. Foliations play a
fundamental role in algebraic geometry, for example in the proof of
abundance for threefolds and to a solution of the Green-Griffiths
conjecture for surfaces of general type with positive Segre class.
The purpose of this volume is to foster communication and enable
interactions between experts who work on holomorphic foliations and
birational geometry, and to bring together leading researchers to
demonstrate the powerful connection of ideas, methods, and goals
shared by these two areas of study.
This book collects the scientific contributions of a group of
leading experts who took part in the INdAM Meeting held in Cortona
in September 2014. With combinatorial techniques as the central
theme, it focuses on recent developments in configuration spaces
from various perspectives. It also discusses their applications in
areas ranging from representation theory, toric geometry and
geometric group theory to applied algebraic topology.
This book provides a first course on lattices - mathematical
objects pertaining to the realm of discrete geometry, which are of
interest to mathematicians for their structure and, at the same
time, are used by electrical and computer engineers working on
coding theory and cryptography. The book presents both fundamental
concepts and a wealth of applications, including coding and
transmission over Gaussian channels, techniques for obtaining
lattices from finite prime fields and quadratic fields,
constructions of spherical codes, and hard lattice problems used in
cryptography. The topics selected are covered in a level of detail
not usually found in reference books. As the range of applications
of lattices continues to grow, this work will appeal to
mathematicians, electrical and computer engineers, and graduate or
advanced undergraduate in these fields.
This book explores the theory and application of locally nilpotent
derivations, a subject motivated by questions in affine algebraic
geometry and having fundamental connections to areas such as
commutative algebra, representation theory, Lie algebras and
differential equations. The author provides a unified treatment of
the subject, beginning with 16 First Principles on which the theory
is based. These are used to establish classical results, such as
Rentschler's Theorem for the plane and the Cancellation Theorem for
Curves. More recent results, such as Makar-Limanov's theorem for
locally nilpotent derivations of polynomial rings, are also
discussed. Topics of special interest include progress in
classifying additive actions on three-dimensional affine space,
finiteness questions (Hilbert's 14th Problem), algorithms, the
Makar-Limanov invariant, and connections to the Cancellation
Problem and the Embedding Problem. A lot of new material is
included in this expanded second edition, such as canonical
factorization of quotient morphisms, and a more extended treatment
of linear actions. The reader will also find a wealth of examples
and open problems and an updated resource for future
investigations.
Customarily, the framework of algebraic geometry has been worked
over an algebraically closed field of characteristic zero, say,
over the complex number field. However, over a field of positive
characteristics, many unpredictable phenomena arise where analyses
will lead to further developments.In the present book, we consider
first the forms of the affine line or the additive group,
classification of such forms and detailed analysis. The forms of
the affine line considered over the function field of an algebraic
curve define the algebraic surfaces with fibrations by curves with
moving singularities. These fibrations are investigated via the
Mordell-Weil groups, which are originally introduced for elliptic
fibrations.This is the first book which explains the phenomena
arising from purely inseparable coverings and Artin-Schreier
coverings. In most cases, the base surfaces are rational, hence the
covering surfaces are unirational. There exists a vast, unexplored
world of unirational surfaces. In this book, we explain the
Frobenius sandwiches as examples of unirational surfaces.Rational
double points in positive characteristics are treated in detail
with concrete computations. These kinds of computations are not
found in current literature. Readers, by following the computations
line after line, will not only understand the peculiar phenomena in
positive characteristics, but also understand what are crucial in
computations. This type of experience will lead the readers to find
the unsolved problems by themselves.
The International Mathematical Olympiad (IMO) is the World
Championship Competition for High School students, and is held
annually in a different country. More than eighty countries are
involved.
Containing numerous exercises, illustrations, hints and solutions,
presented in a lucid and thought- provoking style, this text
provides a wide range of skills required in competitions such as
the Mathematical Olympiad.
More than fifty problems in Euclidean geometry invo9lving integers
and rational numbers are presented. Early chapters cover elementary
problems while later sections break new ground in certain areas and
area greater challenge for the more adventurous reader. The text is
ideal for Mathematical
Olympiad training and also serves as a supplementary text for
student in pure mathematics, particularly number theory and
geometry.
Dr. Christopher Bradley was formerly a Fellow and Tutor in
Mathematics at Jesus College, Oxford, Deputy Leader of the British
Mathematical Olympiad Team and for several years Secretary of the
British Mathematical Olympiad Committee.
This book consists of both expository and research articles
solicited from speakers at the conference entitled "Arithmetic and
Ideal Theory of Rings and Semigroups," held September 22-26, 2014
at the University of Graz, Graz, Austria. It reflects recent trends
in multiplicative ideal theory and factorization theory, and brings
together for the first time in one volume both commutative and
non-commutative perspectives on these areas, which have their roots
in number theory, commutative algebra, and algebraic geometry.
Topics discussed include topological aspects in ring theory, Prufer
domains of integer-valued polynomials and their monadic submonoids,
and semigroup algebras. It will be of interest to practitioners of
mathematics and computer science, and researchers in multiplicative
ideal theory, factorization theory, number theory, and algebraic
geometry.
The purpose of this monograph is two-fold: it introduces a
conceptual language for the geometrical objects underlying Painleve
equations, and it offers new results on a particular Painleve III
equation of type PIII (D6), called PIII (0, 0, 4, 4), describing
its relation to isomonodromic families of vector bundles on P1 with
meromorphic connections. This equation is equivalent to the radial
sine (or sinh) Gordon equation and, as such, it appears widely in
geometry and physics. It is used here as a very concrete and
classical illustration of the modern theory of vector bundles with
meromorphic connections. Complex multi-valued solutions on C* are
the natural context for most of the monograph, but in the last four
chapters real solutions on R>0 (with or without singularities)
are addressed. These provide examples of variations of TERP
structures, which are related to tt geometry and harmonic bundles.
As an application, a new global picture o0 is given.
This book provides a multitude of geometric constructions usually
encountered in civil engineering and surveying practice. A detailed
geometric solution is provided to each construction as well as a
step-by-step set of programming instructions for incorporation into
a computing system. The volume is comprised of 12 chapters and
appendices that may be grouped in three major parts: the first is
intended for those who love geometry for its own sake and its
evolution through the ages, in general, and, more specifically,
with the introduction of the computer. The second section addresses
geometric features used in the book and provides support procedures
used by the constructions presented. The remaining chapters and the
appendices contain the various constructions. The volume is ideal
for engineering practitioners in civil and construction engineering
and allied areas.
An exploration of mathematical style through 99 different proofs of
the same theorem This book offers a multifaceted perspective on
mathematics by demonstrating 99 different proofs of the same
theorem. Each chapter solves an otherwise unremarkable equation in
distinct historical, formal, and imaginative styles that range from
Medieval, Topological, and Doggerel to Chromatic, Electrostatic,
and Psychedelic. With a rare blend of humor and scholarly aplomb,
Philip Ording weaves these variations into an accessible and
wide-ranging narrative on the nature and practice of mathematics.
Inspired by the experiments of the Paris-based writing group known
as the Oulipo-whose members included Raymond Queneau, Italo
Calvino, and Marcel Duchamp-Ording explores new ways to examine the
aesthetic possibilities of mathematical activity. 99 Variations on
a Proof is a mathematical take on Queneau's Exercises in Style, a
collection of 99 retellings of the same story, and it draws
unexpected connections to everything from mysticism and technology
to architecture and sign language. Through diagrams, found
material, and other imagery, Ording illustrates the flexibility and
creative potential of mathematics despite its reputation for
precision and rigor. Readers will gain not only a bird's-eye view
of the discipline and its major branches but also new insights into
its historical, philosophical, and cultural nuances. Readers, no
matter their level of expertise, will discover in these proofs and
accompanying commentary surprising new aspects of the mathematical
landscape.
This title introduces the theory of arc schemes in algebraic
geometry and singularity theory, with special emphasis on recent
developments around the Nash problem for surfaces. The main
challenges are to understand the global and local structure of arc
schemes, and how they relate to the nature of the singularities on
the variety. Since the arc scheme is an infinite dimensional
object, new tools need to be developed to give a precise meaning to
the notion of a singular point of the arc scheme.Other related
topics are also explored, including motivic integration and dual
intersection complexes of resolutions of singularities. Written by
leading international experts, it offers a broad overview of
different applications of arc schemes in algebraic geometry,
singularity theory and representation theory.
This book introduces the reader to basic notions of integrable
techniques for one-dimensional quantum systems. In a pedagogical
way, a few examples of exactly solvable models are worked out to go
from the coordinate approach to the Algebraic Bethe Ansatz, with
some discussion on the finite temperature thermodynamics. The aim
is to provide the instruments to approach more advanced books or to
allow for a critical reading of research articles and the
extraction of useful information from them. We describe the
solution of the anisotropic XY spin chain; of the Lieb-Liniger
model of bosons with contact interaction at zero and finite
temperature; and of the XXZ spin chain, first in the coordinate and
then in the algebraic approach. To establish the connection between
the latter and the solution of two dimensional classical models, we
also introduce and solve the 6-vertex model. Finally, the low
energy physics of these integrable models is mapped into the
corresponding conformal field theory. Through its style and the
choice of topics, this book tries to touch all fundamental ideas
behind integrability and is meant for students and researchers
interested either in an introduction to later delve in the advance
aspects of Bethe Ansatz or in an overview of the topic for
broadening their culture.
As in the previous Seminar Notes, the current volume reflects
general trends in the study of Geometric Aspects of Functional
Analysis, understood in a broad sense. A classical theme in the
Local Theory of Banach Spaces which is well represented in this
volume is the identification of lower-dimensional structures in
high-dimensional objects. More recent applications of
high-dimensionality are manifested by contributions in Random
Matrix Theory, Concentration of Measure and Empirical Processes.
Naturally, the Gaussian measure plays a central role in many of
these topics, and is also studied in this volume; in particular,
the recent breakthrough proof of the Gaussian Correlation
Conjecture is revisited. The interplay of the theory with Harmonic
and Spectral Analysis is also well apparent in several
contributions. The classical relation to both the primal and dual
Brunn-Minkowski theories is also well represented, and related
algebraic structures pertaining to valuations and valent functions
are discussed. All contributions are original research papers and
were subject to the usual refereeing standards.
The classification of algebraic surfaces is an intricate and
fascinating branch of mathematics, developed over more than a
century and still an active area of research today. In this book,
Professor Beauville gives a lucid and concise account of the
subject, expressed simply in the language of modern topology and
sheaf theory, and accessible to any budding geometer. A chapter on
preliminary material ensures that this volume is self-contained
while the exercises succeed both in giving the flavor of the
classical subject, and in equipping the reader with the techniques
needed for research. The book is aimed at graduate students in
geometry and topology.
Providing a timely description of the present state of the art of
moduli spaces of curves and their geometry, this volume is written
in a way which will make it extremely useful both for young people
who want to approach this important field, and also for established
researchers, who will find references, problems, original
expositions, new viewpoints, etc. The book collects the lecture
notes of a number of leading algebraic geometers and in particular
specialists in the field of moduli spaces of curves and their
geometry. This is an important subject in algebraic geometry and
complex analysis which has seen spectacular developments in recent
decades, with important applications to other parts of mathematics
such as birational geometry and enumerative geometry, and to other
sciences, including physics. The themes treated are classical but
with a constant look to modern developments (see Cascini, Debarre,
Farkas, and Sernesi's contributions), and include very new
material, such as Bridgeland stability (see Macri's lecture notes)
and tropical geometry (see Chan's lecture notes).
This volume is based on four advanced courses held at the Centre de
Recerca Matematica (CRM), Barcelona. It presents both background
information and recent developments on selected topics that are
experiencing extraordinary growth within the broad research area of
geometry and quantization of moduli spaces. The lectures focus on
the geometry of moduli spaces which are mostly associated to
compact Riemann surfaces, and are presented from both classical and
quantum perspectives.
|
You may like...
Autopsy
Patricia Cornwell
Paperback
R436
Discovery Miles 4 360
Die Bewonderaar
Erla-Mari Diedericks
Paperback
(1)
R300
R281
Discovery Miles 2 810
Lies He Told Me
James Patterson, David Ellis
Paperback
R370
R342
Discovery Miles 3 420
In Too Deep
Lee Child, Andrew Child
Paperback
R395
R300
Discovery Miles 3 000
A Quiet Man
Tom Wood
Paperback
R427
R393
Discovery Miles 3 930
Zero Hour
Don Bentley
Paperback
R459
R423
Discovery Miles 4 230
Homeland
Karin Brynard
Paperback
R290
R131
Discovery Miles 1 310
The Spy Coast
Tess Gerritsen
Paperback
R380
R300
Discovery Miles 3 000
|