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arXiv · 2304.13821

Singular holomorphic Morse inequalities on non-compact manifolds

Dan Coman·George Marinescu·Huan Wang
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Abstract

We study asymptotic estimates of the dimension of cohomology on possibly non-compact complex manifolds for line bundles endowed with Hermitian metrics with algebraic singularities. We give a unified approach to establishing singular holomorphic Morse inequalities for hyperconcave manifolds, pseudoconvex domains, $q$-convex manifolds and $q$-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.

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Dan Coman, George Marinescu, Huan Wang. 2023-04-26. Singular holomorphic Morse inequalities on non-compact manifolds. https://doi.org/10.59277/rrmpa.2023.61.82

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