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arXiv · 1810.09881

The growth of dimension of cohomology of semipositive line bundles on Hermitian manifolds

Huan Wang
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Abstract

In this paper, we study the dimension of cohomology of semipositive line bundles over Hermitian manifolds, and obtain an asymptotic estimate for the dimension of the space of harmonic $(0,q)$-forms with values in high tensor powers of a semipositive line bundle when the fundamental estimate holds. As applications, we estimate the dimension of cohomology of semipositive line bundles on $q$-convex manifolds, pseudo-convex domains, weakly $1$-complete manifolds and complete manifolds. We also obtain the estimate of cohomology on compact manifolds with semipositive line bundles endowed with a Hermitian metric with analytic singularities and the related vanishing theorems.

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Huan Wang. 2018-10-23. The growth of dimension of cohomology of semipositive line bundles on Hermitian manifolds. https://doi.org/10.1007/s00209-020-02512-w

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