Holomorphic Morse Inequalities and Bergman Kernels

This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. The point of view comes from local index theory. The book opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of co...