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Leray–Hirsch theorem and blow-up formula for Dolbeault cohomology

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Abstract

We prove a theorem of Leray–Hirsch type and give an explicit blow-up formula for Dolbeault cohomology on (not necessarily compact) complex manifolds. We give applications to strongly q-complete manifolds and the \(\partial \bar{\partial }\)-lemma.

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Acknowledgements

I would like to express my gratitude to Prof. Fu, Jixiang for his encouragement and support and thank School of Mathematical Science of Fudan University for the hospitality during my visit. In particular, I would like to thank Prof. Rao, Sheng and Dr. Yang, Xiang-Dong for many useful discussions and sending me the newest versions of their articles [28, 29, 37]. I would like to thank the referee for valuable suggestions and careful reading of my manuscript.

Funding

The author is supported by the Natural Science Foundation of Shanxi Province of China (Grant No. 201901D111141).

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  1. Department of Mathematics, North University of China, Taiyuan, 030051, Shanxi, People’s Republic of China

    Lingxu Meng

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Meng, L. Leray–Hirsch theorem and blow-up formula for Dolbeault cohomology. Annali di Matematica 199, 1997–2014 (2020). https://doi.org/10.1007/s10231-020-00953-y

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