Hardcover ISBN:  9780821832400 
Product Code:  CRMM/21 
List Price:  $53.00 
MAA Member Price:  $47.70 
AMS Member Price:  $42.40 
Electronic ISBN:  9781470438661 
Product Code:  CRMM/21.E 
List Price:  $50.00 
MAA Member Price:  $45.00 
AMS Member Price:  $40.00 

Book DetailsCRM Monograph SeriesVolume: 21; 2003; 136 ppMSC: Primary 53; Secondary 14; 57; 81;
This book is written by a wellknown expert in classical algebraic geometry. Tyurin's research was specifically in explicit computations to vector bundles on algebraic varieties. This is the only available monograph written from his unique viewpoint.
Ordinary (abelian) theta functions describe properties of moduli spaces of onedimensional vector bundles on algebraic curves. Nonabelian theta functions, which are the main topic of this book, play a similar role in the study of higherdimensional vector bundles. The book presents various aspects of the theory of nonabelian theta functions and the moduli spaces of vector bundles, including their applications to problems of quantization and to classical and quantum conformal field theories.
The book is an important source of information for specialists in algebraic geometry and its applications to mathematical aspects of quantum field theory.ReadershipGraduate students and research mathematicians interested in algebraic geometry and its applications to mathematical physics.

Table of Contents

Chapters

Quantization procedure

Algebraic curves = Riemann surfaces

Nonabelian theta functions

Symplectic geometry of moduli spaces of vector bundles

Two versions of CQFT

Threevalent graphs

Analytical aspects of the theory of nonabelian theta functions

BPUmap

The main weapon


Additional Material

Reviews

The book opens a beautiful and grandiose view to a fascinating part of geometry, notably symplectic and algebraic geometry, and, as usual in Andrei Tyurin's work, it has a very geometric flavor. ...The ideal reader should preferably dispose of some basic knowledge of classical algebraic geometry or theory of Riemann surfaces and of symplectic geometry, then he will benefit quite a lot from reading this book.
Zentralblatt MATH


Request Review Copy
 Book Details
 Table of Contents
 Additional Material
 Reviews

 Request Review Copy
This book is written by a wellknown expert in classical algebraic geometry. Tyurin's research was specifically in explicit computations to vector bundles on algebraic varieties. This is the only available monograph written from his unique viewpoint.
Ordinary (abelian) theta functions describe properties of moduli spaces of onedimensional vector bundles on algebraic curves. Nonabelian theta functions, which are the main topic of this book, play a similar role in the study of higherdimensional vector bundles. The book presents various aspects of the theory of nonabelian theta functions and the moduli spaces of vector bundles, including their applications to problems of quantization and to classical and quantum conformal field theories.
The book is an important source of information for specialists in algebraic geometry and its applications to mathematical aspects of quantum field theory.
Graduate students and research mathematicians interested in algebraic geometry and its applications to mathematical physics.

Chapters

Quantization procedure

Algebraic curves = Riemann surfaces

Nonabelian theta functions

Symplectic geometry of moduli spaces of vector bundles

Two versions of CQFT

Threevalent graphs

Analytical aspects of the theory of nonabelian theta functions

BPUmap

The main weapon

The book opens a beautiful and grandiose view to a fascinating part of geometry, notably symplectic and algebraic geometry, and, as usual in Andrei Tyurin's work, it has a very geometric flavor. ...The ideal reader should preferably dispose of some basic knowledge of classical algebraic geometry or theory of Riemann surfaces and of symplectic geometry, then he will benefit quite a lot from reading this book.
Zentralblatt MATH