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Vanishing theorem on parabolic Kähler manifolds

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Abstract

In this article, we consider the semipositive (resp. nef) line bundle on compact Kähler parabolic (resp. hyperbolic) manifolds. We prove some vanishing theorems for the \(L^{2}\)-harmonic (n, q)-form of the holomorphic line bundles over complete Kähler manifolds.

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Acknowledgements

I would also like to thank the anonymous referee for careful reading of my manuscript and helpful comments. This work was supported in part by NSF of China (No. 12271496) and the Youth Innovation Promotion Association CAS, the Fundamental Research Funds of the Central Universities, the USTC Research Funds of the Double First-Class Initiative. My manuscript has no associated data.

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  1. School of Mathematical Sciences, CAS Key Laboratory of Wu Wen-Tsun Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui, People’s Republic of China

    Teng Huang

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  1. Teng Huang
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Correspondence to Teng Huang.

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Huang, T. Vanishing theorem on parabolic Kähler manifolds. Geom Dedicata 218, 25 (2024). https://doi.org/10.1007/s10711-023-00872-1

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