Holomorphic Morse Inequalities and Bergman Kernels

By Xiaonan Ma

This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. The point of view comes from local index theory. The book opens perspectives on several active areas of research in complex, K hler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete K hler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.

• Format: Hardcover
• Language: English
• ISBN: 3764380969
• ISBN13: 9783764380960
• Release Date: July 2007
• Publisher: Birkhauser
• Length: 422 Pages
• Weight: 1.95 lbs.
• Dimensions: 1.1" x 6.4" x 9.3"