Several Complex Variables With Connections To Algebraic Geometry And Lie Groups PDF Download
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Author | : Joseph L. Taylor |
Publisher | : American Mathematical Soc. |
Total Pages | : 530 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 082183178X |
Download Several Complex Variables with Connections to Algebraic Geometry and Lie Groups Book in PDF, ePub and Kindle
This text presents an integrated development of core material from several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraicsheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest arethe last three chapters, which are devoted to applications of the preceding material to the study of the structure theory and representation theory of complex semisimple Lie groups. Included are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem,which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for theexpert.
Author | : Michael Schneider |
Publisher | : Cambridge University Press |
Total Pages | : 582 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780521770866 |
Download Several Complex Variables Book in PDF, ePub and Kindle
Expository articles on Several Complex Variables and its interactions with PDEs, algebraic geometry, number theory, and differential geometry, first published in 2000.
Author | : G.M. Khenkin |
Publisher | : Springer Science & Business Media |
Total Pages | : 265 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 364261308X |
Download Several Complex Variables III Book in PDF, ePub and Kindle
We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space
Author | : Yum-Tong Siu |
Publisher | : American Mathematical Soc. |
Total Pages | : 312 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : 082181446X |
Download Complex Analysis of Several Variables Book in PDF, ePub and Kindle
Presents a collection of papers from the Symposium on Several Complex Variables held April 12-15, 1983 in Madison, Wisconsin. This book contains a selection of the presented papers as well as some contributed papers.
Author | : Wolfgang Ebeling |
Publisher | : American Mathematical Soc. |
Total Pages | : 334 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0821833197 |
Download Functions of Several Complex Variables and Their Singularities Book in PDF, ePub and Kindle
The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.
Author | : Steven George Krantz |
Publisher | : American Mathematical Soc. |
Total Pages | : 586 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827243 |
Download Function Theory of Several Complex Variables Book in PDF, ePub and Kindle
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
Author | : Pierre Lelong |
Publisher | : Springer Science & Business Media |
Total Pages | : 283 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642703445 |
Download Entire Functions of Several Complex Variables Book in PDF, ePub and Kindle
I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions.
Author | : D. Sundararaman |
Publisher | : Pitman Publishing |
Total Pages | : 202 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : |
Download Topics in Several Complex Variables Book in PDF, ePub and Kindle
This book provides an overview of currently active and rapidly developing areas of several complex variables, differential geometry and group representations. The featured papers are written by experts and researchers and give new insights into the topics they deal with and new results of the relevant theories and problems. Apart from the applications to the traditional area of mathematical physics, applications to the new area of computerized tomography are also included.
Author | : Raghavan Narasimhan |
Publisher | : University of Chicago Press |
Total Pages | : 185 |
Release | : 1971 |
Genre | : Mathematics |
ISBN | : 0226568172 |
Download Several Complex Variables Book in PDF, ePub and Kindle
Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.
Author | : Takeo Ōsawa |
Publisher | : American Mathematical Soc. |
Total Pages | : 148 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 9780821820988 |
Download Analysis of Several Complex Variables Book in PDF, ePub and Kindle
An expository account of the basic results in several complex variables that are obtained by L℗ methods.