Holomorphic Morse Inequalities and Bergman Kernels

  • Xiaonan Ma
  • George Marinescu

Part of the Progress in Mathematics book series (PM, volume 254)

Table of contents

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.


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

Authors and affiliations

  • Xiaonan Ma
    • 1
  • George Marinescu
    • 2
  1. 1.Centre de Mathématiques Laurent Schwartz (C.M.L.S.)École PolytechniquePalaiseau CedexFrance
  2. 2.Mathematisches InstitutUniversität zu KölnKölnGermany

Bibliographic information