%0 Journal Article
%T Bergman kernels and local holomorphic Morse inequalities
%A Robert Berman
%J Mathematics
%D 2002
%I arXiv
%X Let X be a hermitian manifold and let L^k be a high power of a hermitian line bundle over X. Local versions of Demailly's holomorphic Morse inequalities are presented - after integration they yield the usual inequalities. The local weak inequalities hold on any hermitian manifold X, regardless of compactness and completeness. The proofs, which are elementary, are based on a new approach to pointwise Bergman kernel estimates, where the kernels are estimated by a model kernel in the standard complex space C^n.
%U http://arxiv.org/abs/math/0211235v1