Cohomology of Quotients in Symplectic and Algebraic Geometry

by Frances Clare Kirwan

Overview

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant theory associates to reductive group actions on nonsingular complex projective varieties. These quotient 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.

Product Details

ISBN-13:	9780691083704
Publisher:	Princeton University Press
Publication date:	12/21/1984
Series:	Mathematical Notes , #104
Pages:	216
Product dimensions:	6.00(w) x 9.25(h) x (d)