The harmonic theory on a vector bundle with singular Hermitian metrics and positivity

2021/02/08 by Jingcao Wu, Wu, Jingcao
Mathematics · Physics and Astronomy · #32J25 #32Q10 #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2102.04037

openalex publication_date 2021/02/08 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28

Abstract

Let E be a holomorphic vector bundle endowed with a singular Hermitian metric H. In this paper, we develop the harmonic theory on (E,H). Then we extend several canonical results of J. Kollár and K. Takegoshi to this situation. In the end, we generalise Nakano's vanishing theorem.

Citations

• An alternative approach on the singular metric on a vector bundle

Related

• Positivity of Singular Hermitian Metrics for Holomorphic Vector Bundles
• An alternative approach on the singular metric on a vector bundle
• Singular hermitian metrics on vector bundles
• Nakano positivity of singular Hermitian metrics: Approximations and applications
• Nadel-Nakano vanishing theorems of vector bundles with singular Hermitian metrics