Overview

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

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9786611140267

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