Curvature positivity of invariant direct images of Hermitian vector bundles

Fusheng Deng; Jinjin Hu; Weiwen Jiang

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arXiv · 2009.01173

Curvature positivity of invariant direct images of Hermitian vector bundles

Fusheng Deng·Jinjin Hu·Weiwen Jiang

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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. The two main ingredients in our method are H\"ormander's $L^2$ theory of $\bar\partial$ and the recent work of Deng-Ning-Zhang-Zhou on characterization of Nakano positivity of Hermitian holomorphic vector bundles.

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Fusheng Deng, Jinjin Hu, Weiwen Jiang. 2020-09-01. Curvature positivity of invariant direct images of Hermitian vector bundles. https://arxiv.org/abs/2009.01173

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