Holomorphic Morse Inequalities and Bergman Kernels

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 i...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Ma, Xiaonan (Autor), Marinescu, George (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2007.
Edición:1st ed. 2007.
Colección:Progress in Mathematics, 254
Temas:
Geometry, Differential.
Functions of complex variables.
Global analysis (Mathematics).
Manifolds (Mathematics).
Differential Geometry.
Several Complex Variables and Analytic Spaces.
Global Analysis and Analysis on Manifolds.
Acceso en línea:Texto Completo
Descripción
Sumario: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.
Descripción Física:XIII, 422 p. online resource.
ISBN:9783764381158
ISSN:2296-505X ;

Ejemplares similares