English

Singular holomorphic Morse inequalities on non-compact manifolds

Complex Variables 2023-11-28 v2 Algebraic Geometry

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, qq-convex manifolds and qq-concave manifolds, and we generalize related estimates of Berndtsson. We also consider the case of metrics with more general than algebraic singularities.

Keywords

Cite

@article{arxiv.2304.13821,
  title  = {Singular holomorphic Morse inequalities on non-compact manifolds},
  author = {Dan Coman and George Marinescu and Huan Wang},
  journal= {arXiv preprint arXiv:2304.13821},
  year   = {2023}
}

Comments

Dedicated to the memory of Mihnea Coltoiu. 15 pages; v.2 is a final update to agree with the published paper

R2 v1 2026-06-28T10:19:04.826Z