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Birkhäuser - Birkhäuser Mathematics | Holomorphic Morse Inequalities and Bergman Kernels

Holomorphic Morse Inequalities and Bergman Kernels

Winner of the Ferran Sunyer i Balaguer Prize 2006

Series: Progress in Mathematics, Vol. 254

Zhang, Weiping, Marinescu, George

2007, XIII, 422 p.

A product of Birkhäuser Basel
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  • New approach to the holomorphic Morse inequalities and Bergman kernel expansions
  • Exploits the analytic localization techniques in local index theory developed by Bismut-Lebeau
  • Most of the material appears for the first time in book form

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.

Content Level » Research

Keywords » Analytic torsion - Bergman kernel - Complex analysis - Morse theory - curvature - manifold - symplectic geometry

Related subjects » Birkhäuser Mathematics

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