ENGLISH

Holomorphic Morse Inequalities and Bergman Kernels

By Xiaonan Ma , George Marinescu

Book information

Publisher
Birkhäuser
Year
2007
ISBN
9783764380960, 3764380969
Open Library ID
OL12867089M
Language
english
Format
PDF
Filesize
5 MB (5288793 bytes)
Series
Progress in Mathematics
Edition
1
Pages
432\432
Library
mexmat
Time added
2009-11-09 02:42:13

Description

This book gives for the first time a self-contained and unified approach to holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel, and presents also various applications.The main analytic tool is the analytic localization technique in local index theory developed by Bismut-Lebeau. The book includes the most recent results in the field and therefore opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are included, e.g., an analytic proof of the Kodaira embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, a compactification of complete Kähler manifolds of pinched negative curvature, the Berezin-Toeplitz quantization, weak Lefschetz theorems, and the asymptotics of the Ray-Singer analytic torsion.

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