Science/Engineering Vertex Algebras and Algebraic Curves (0821836749)

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Vertex Algebras and Algebraic Curves

Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence. The book is suitable for graduate students and research mathematicians interested in representation theory, algebraic geometry, and mathematical physics. For more information, visit www.math.berkeley.edu/ frenkel/book.

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	Encyclopedias Algebraic Geometry I: Algebraic Curves Algebraic Manifolds and Schemes (Encyclopaedia of Mathematical Sciences) Algebraic Geometry I: Algebraic Curves Algebraic Manifolds and Schemes (Encyclopaedia of Mathematical Sciences)Springer \| 1994 \| ISBN: 0387519955 \| Pages: 307 \| DJVU \| 3.71 MBThis volume of the Encyclopaedia consists of two parts. The first ...
	Science/Engineering Vertex Algebras for Beginners (University Lecture Series) - 2nd ed. Vertex Algebras for Beginners (University Lecture Series) - 2nd ed. Publisher: American Mathematical Society \| ISBN: 082181396X \| edition 1998 \| DJVU \| 201 pages \| 1,35 mbThis is a revised and expanded edition of Kac's original introductio ...
	Nonfiction Algebraic Curves: an Introduction to Algebraic Geometry The aim of these notes is to develop the theory of algebraic curves from the viewpoint of modern algebraic geometry, but without excessive prerequisites. We have assumed that the reader is familiar with some basic properties of rings, ideal ...
	Technical Vertex Operator Algebras and the Monster, Volume 134 (Pure and Applied Mathematics) ISBN: 0122670655 Publisher: Academic Press Author: Igor Frenkel, James Lepowsky, Arne MeurmanDescription:This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, f ...
	Mathematics Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians Parshin A.N., Shafarevich I.R (Ed.) ¡°Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians" Springer \| 1997-12-16 \| ISBN: 3540546812 \| Djvu \| 278 pages \| 2,4 Mb The first contribution of this EMS vo ...
	Mathematics ALGEBRAIC CURVES An Introduction to Algebraic Geometry ALGEBRAIC CURVES An Introduction to Algebraic GeometryPublisher: arXiv \| ISBN: N\A \| edition 1998 \| PDF \| 129 pages \| 1,7 mbThe author discusses: Homogeneous varieties, Topology and consequences Projective differential invariants, Varietie ...

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