Author : Frances Clare Kirwan
Publisher : Princeton University Press
ISBN 13 : 0691214565
Total Pages : 216 pages
Book Rating : 4.6/5 (912 download)
Book Synopsis Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31 by : Frances Clare Kirwan
Download or read book Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31 written by Frances Clare Kirwan and published by Princeton University Press. This book was released on 2020-06-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.