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The growth of dimension of cohomology of semipositive line bundles on Hermitian manifolds

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Abstract

In this paper, we study the dimension of cohomology of semipositive line bundles over Hermitian manifolds, and obtain an asymptotic estimate for the dimension of the space of harmonic (0, q)-forms with values in high tensor powers of a semipositive line bundle when the fundamental estimate holds. As applications, we estimate the dimension of cohomology of semipositive line bundles on q-convex manifolds, pseudo-convex domains, weakly 1-complete manifolds and complete manifolds. We also obtain the estimate of cohomology on compact manifolds with semipositive line bundles endowed with a Hermitian metric with analytic singularities and related results.

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Acknowledgements

The author is grateful to Professor George Marinescu for his support and encouragement over years. The author thanks Professor Xianzhe Dai for helpful discussion and enlightened comments. This work was partially supported by Taiwan Ministry of Science and Technology project 108-2811-M-001-577, Albert’s Researcher Reunion Grant and the Mobility Grant within measure 6 of the Excellence Initiative of University of Cologne.

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  1. Institute of Mathematics, Academia Sinica, Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei, 10617, Taiwan

    Huan Wang

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  1. Huan Wang
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Correspondence to Huan Wang.

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Wang, H. The growth of dimension of cohomology of semipositive line bundles on Hermitian manifolds. Math. Z. 297, 339–360 (2021). https://doi.org/10.1007/s00209-020-02512-w

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