Singular holomorphic Morse inequalities on non-compact manifolds

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.

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