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An \(L^2\) Dolbeault lemma and its applications to vanishing theorems

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Abstract

In this paper, we will first build an \(L^2\) Dolbeault lemma by analytic methods and Hörmander \(L^2\) estimates. Then as applications, we will prove some log Nadel type vanishing theorems on compact Kähler manifolds and some log Kawamata–Viehweg type vanishing theorems on projective manifolds. Some log Nakano–Demailly type vanishing theorems for vector bundles will be also discussed by the same methods; one of which generalizes the original Nakano vanishing theorem on compact Kähler manifolds.

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Acknowledgements

The author would like to thank the referee for carefully reading the paper and for valuable suggestions.

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  1. Institute of Mathematics, Hunan University, Changsha, 410082, China

    Chunle Huang

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  1. Chunle Huang
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Correspondence to Chunle Huang.

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Huang, C. An \(L^2\) Dolbeault lemma and its applications to vanishing theorems. Ann Glob Anal Geom 57, 205–215 (2020). https://doi.org/10.1007/s10455-019-09695-4

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  • DOI: https://doi.org/10.1007/s10455-019-09695-4

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