Holomorphic Morse Inequalities and Bergman Kernels [electronic resource] /
Ma, Xiaonan.author.
Marinescu, George.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
Demailly's Holomorphic Morse Inequalities -- Characterization of Moishezon Manifolds -- Holomorphic Morse Inequalities on Non-compact Manifolds -- Asymptotic Expansion of the Bergman Kernel -- Kodaira Map -- Bergman Kernel on Non-compact Manifolds -- Toeplitz Operators -- Bergman Kernels on Symplectic Manifolds.
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.
Differential geometry.
Functions of complex variables.
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential Geometry.
Several Complex Variables and Analytic Spaces.
Global Analysis and Analysis on Manifolds.