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Local Demailly-Bouche's holomorphic morse inequalities
by Zhiwei Wang

Vol. 12 No. 4 (2017) P.339~P.360
 DOI: https://doi.org/10.21915/BIMAS.2017404 10.21915/BIMAS.2017404

ABSTRACT

Let $(X,\omega)$ be a Hermitian manifold and let $(E,h^E)$, $(F,h^F)$ be two Hermitian holomorphic line bundle over $X$. Suppose that the maximal rank of the Chern curvature $c(E)$ of $E$ is $r$, and the kernel of $c(E)$ is foliated. In this paper, local versions of Demailly-Bouche's holomorphic Morse inequalities are presented. The local version holds on any Hermitian manifold regardless of compactness and completeness. The proof is a generalization of Berman's method to derive Demailly's holomorphic Morse inequalities.

KEYWORDS
Bergman kernel, Local holomorphic Morse inequalities, Localization

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 32A25, 32L10, 32L20

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