Item description for Holomorphic Morse Inequalities and Bergman Kernels (Progress in Mathematics) by Xiaonan Ma & George Marinescu...
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, Khler 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 Khler 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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Est. Packaging Dimensions: Length: 1" Width: 6.25" Height: 9.25" Weight: 1.95 lbs.
Release Date Sep 14, 2007
Publisher Birkhäuser Basel
ISBN 3764380969 ISBN13 9783764380960