Overview
- Most of the material appears for the first time in book form
- New approach to the holomorphic Morse inequalities and Bergman kernel expansions
- Exploits the analytic localization techniques in local index theory developed by Bismut-Lebeau
- Includes supplementary material: sn.pub/extras
Part of the book series: Progress in Mathematics (PM, volume 254)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Holomorphic Morse Inequalities and Bergman Kernels
Authors: Xiaonan Ma, George Marinescu
Series Title: Progress in Mathematics
DOI: https://doi.org/10.1007/978-3-7643-8115-8
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkh�user Basel 2007
Hardcover ISBN: 978-3-7643-8096-0Published: 19 July 2007
eBook ISBN: 978-3-7643-8115-8Published: 14 December 2007
Series ISSN: 0743-1643
Series E-ISSN: 2296-505X
Edition Number: 1
Number of Pages: XIII, 422
Topics: Differential Geometry, Several Complex Variables and Analytic Spaces, Global Analysis and Analysis on Manifolds