Cohomology of quotients in symplectic and algebraic geometry / Frances Clare Kirwan.

Format:

Book

Author/Creator:

Kirwan, Frances Clare, 1959- author.

Series:

Mathematical notes (Princeton University Press) ; 31.

Mathematical notes ; 31

Language:

English

Subjects (All):

Algebraic varieties.

Symplectic manifolds.

Homology theory.

Group schemes (Mathematics).

Physical Description:

1 online resource (218 pages) : illustrations.

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1984.

Summary:

These notes describe a general procedure for calculating the Betti numbers of the projective "ient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These "ient varieties are interesting in particular because of their relevance to moduli problems in algebraic geometry. The author describes two different approaches to the problem. One is purely algebraic, while the other uses the methods of symplectic geometry and Morse theory, and involves extending classical Morse theory to certain degenerate functions.

Contents:

Frontmatter

Contents

Introduction

Part I. The symplectic approach*

Part II. The algebraic approach.

References

Notes:

Description based on print version record.

ISBN:

9780691214566

0691214565