Vertex Algebras and Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Vertex Algebras and Algebraic Curves write by Edward Frenkel. This book was released on 2004-08-25. Vertex Algebras and Algebraic Curves available in PDF, EPUB and Kindle. 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.
Vertex Algebras and Algebraic Curves
Vertex Algebras and Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Vertex Algebras and Algebraic Curves write by Edward Frenkel. This book was released on . Vertex Algebras and Algebraic Curves available in PDF, EPUB and Kindle. 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.
Vertex Algebras for Beginners
Vertex Algebras for Beginners - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Vertex Algebras for Beginners write by Victor G. Kac. This book was released on 1998. Vertex Algebras for Beginners available in PDF, EPUB and Kindle. Based on courses given by the author at MIT and at Rome University in spring 1997, this book presents an introduction to algebraic aspects of conformal field theory. It includes material on the foundations of a rapidly growing area of algebraic conformal theory.
Introduction to Algebraic Curves
Introduction to Algebraic Curves - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Algebraic Curves write by Phillip A. Griffiths. This book was released on 1989. Introduction to Algebraic Curves available in PDF, EPUB and Kindle. This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here, the book provides a solid foundation to proceed to more advanced texts in general algebraic geometry, complex manifolds, and Riemann surfaces, as well as algebraic curves. Containing numerous exercises this book would make an excellent introductory text.
Algebraic Geometry for Scientists and Engineers
Algebraic Geometry for Scientists and Engineers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Geometry for Scientists and Engineers write by Shreeram Shankar Abhyankar. This book was released on 1990. Algebraic Geometry for Scientists and Engineers available in PDF, EPUB and Kindle. Based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, this book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities.
