Bergman kernels and local holomorphic Morse inequalities

By Robert J. Berman. 2002

52 citations recorded by the source corpus.

Abstract.Let (X,ω) be a hermitian manifold and let Lk be a high power of a hermitian holomorphic line bundle over X. Local versions of Demailly’s holomorphic Morse inequalities (that give bounds on the dimension of the Dolbeault cohomology groups associated to Lk), are presented - after integration they give the usual holomorphic Morse inequalities. The local weak inequalities hold on any hermitian manifold (X,ω), 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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/973feadb977a69ff8bcb7848fc7d6909c10a7a55

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Bergman kernels and equilibrium measures for line bundles over projective manifolds (2007, background): “In [3] the point-wise estimate was shown in the more general setting of ∂-harmonic (0, q)- forms with values in a high power of an Hermitian line bundle.”