Cohomology dimension growth for Nakano $q$-semipositive line bundles

Abstract

We study the cohomology with high tensor powers of Nakano $q$-semipositive line bundles on complex manifolds. We obtain the asymptotic estimates for the dimension of cohomology with high tensor powers of semipositive line bundles over q-convex manifolds and various possibly non-compact complex manifolds, in which the order of estimates are optimal. Besides, estimates for the modified Dirac operator on Nakano $q$-positive line bundle on almost complex manifolds are given.

arXiv admin note: text overlap with arXiv:1810.09881

References in corpus (3)

• On the growth of von Neumann dimension of harmonic spaces of semipositive line bundles over covering manifolds
• The growth of dimension of cohomology of semipositive line bundles on Hermitian manifolds
• Asymptotic estimate of cohomology groups valued in pseudo-effective line bundles

Cited by in corpus (2)

• Szegő kernel asymptotics on some non-compact complete CR manifolds
• On Bergman kernel functions and weak Morse inequalities