2017 / December Volume 12 No.4
Local Demailly-Bouche's holomorphic morse inequalities
| Published Date |
2017 / December
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|---|---|
| Title | Local Demailly-Bouche's holomorphic morse inequalities |
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| Pagination | 339-360 |
| 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.
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| DOI | |
| AMS Subject Classification |
32A25, 32L10, 32L20
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| Received |
2017-06-22
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| Accepted |
2017-12-03
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