Description

Book Synopsis
Presents an integrated development of the theory of 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. This text includes a treatment of the local theory.

Table of Contents
Selected problems in one complex variable Holomorphic functions of several variables Local rings and varieties The Nullstellensatz Dimension Homological algebra Sheaves and sheaf cohomology Coherent algebraic sheaves Coherent analytic sheaves Stein spaces Frechet sheaves--Cartan's theorems Projective varieties Algebraic vs. analytic--Serre's theorems Lie groups and their representations Algebraic groups The Borel-Weil-Bott theorem Bibliography Index.

Several Complex Variables with Connections to

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A Hardback by Joseph L. Taylor

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    Publisher: MP-AMM American Mathematical
    Publication Date: 5/30/2002 12:00:00 AM
    ISBN13: 9780821831786, 978-0821831786
    ISBN10: 082183178X
    Also in:
    Calculus and mathematical analysis Functional analysis and transforms

    Description

    Book Synopsis
    Presents an integrated development of the theory of 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. This text includes a treatment of the local theory.

    Table of Contents
    Selected problems in one complex variable Holomorphic functions of several variables Local rings and varieties The Nullstellensatz Dimension Homological algebra Sheaves and sheaf cohomology Coherent algebraic sheaves Coherent analytic sheaves Stein spaces Frechet sheaves--Cartan's theorems Projective varieties Algebraic vs. analytic--Serre's theorems Lie groups and their representations Algebraic groups The Borel-Weil-Bott theorem Bibliography Index.

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