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

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.

preprint2019arXivOpen access
Huan Wang
math.CVmath.DG
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Huan Wang

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