Curvature positivity of invariant direct images of Hermitian vector bundles

2020/09/01 by Fusheng Deng, Jinjin Hu, Deng, Fusheng +3
Mathematics · #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2009.01173

openalex publication_date 2020/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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 Hörmander's L² theory of ∂ and the recent work of Deng-Ning-Zhang-Zhou on characterization of Nakano positivity of Hermitian holomorphic vector bundles.

Citations

• Log concavity for matrix-valued functions and a matrix-valued Prékopa theorem

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