Progress in Mathematics

Ma, Xiaonan; Marinescu, George

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, Kähler 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 Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.

Details

Published by: Birkhäuser

Publication Date: 2007-07-19

Format: Hardcover

ISBN-13: 9783764380960

DOI: 10.1007/978-3-7643-8115-8

Dimensions: 235cm x155cm

Pages: 422