Progress in Mathematics

Holomorphic Morse Inequalities and Bergman Kernels

Authors: Ma, Xiaonan, Marinescu, George

  • 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
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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.

Table of contents (9 chapters)

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-7643-8115-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-3-7643-8096-0
  • Free shipping for individuals worldwide
  • This title is currently reprinting. You can pre-order your copy now.
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Bibliographic Information

Bibliographic Information
Book Title
Holomorphic Morse Inequalities and Bergman Kernels
Authors
Series Title
Progress in Mathematics
Series Volume
254
Copyright
2007
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-8115-8
DOI
10.1007/978-3-7643-8115-8
Hardcover ISBN
978-3-7643-8096-0
Series ISSN
0743-1643
Edition Number
1
Number of Pages
XIII, 422
Topics