Holomorphic Morse Inequalities and Bergman Kernels
Publication year: 2007
ISBN: 978-3-7643-8115-8
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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.
Subject: Mathematics and Statistics, Analytic torsion, Bergman kernel, Complex analysis, Morse theory, curvature, manifold, symplectic geometry
