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Curvature positivity of invariant direct images of Hermitian vector bundles

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Abstract

We prove that the invariant part, with respect to a compact group action satisfying certain condition, of the direct image of a Nakano positive Hermitian holomorphic vector bundle over a bounded pseudoconvex domain is Nakano positive. We also consider the action of the noncompact group \({\mathbb {R}}^m\) and get the same result for a family of tube domains, which leads to a new method to the matrix-valued Prekopa’s theorem originally proved by Raufi.

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Acknowledgments

The authors are grateful to Professor Jiafu Ning, Zhiwei Wang, and Xiangyu Zhou for helpful discussions and thank the referee for suggesting them consider minimum principle for vector bundles with singular Hermitian metrics. The authors are partially supported by the NSFC grants ( N. 11871451 and 12071310), and by the Fundamental Research Funds for the Central Universities.

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  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Fusheng Deng, Jinjin Hu & Weiwen Jiang

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  1. Fusheng Deng
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  2. Jinjin Hu
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  3. Weiwen Jiang
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Correspondence to Weiwen Jiang.

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Deng, F., Hu, J. & Jiang, W. Curvature positivity of invariant direct images of Hermitian vector bundles. Annali di Matematica 202, 927–937 (2023). https://doi.org/10.1007/s10231-022-01265-z

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  • DOI: https://doi.org/10.1007/s10231-022-01265-z

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