Logarithmic vanishing theorems on compact Kähler manifolds I

2016/11/23 by Chunle Huang, Huang, Chunle, Kefeng Liu +5 · 1 citation
Mathematics · #14F17 #32L20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1611.07671

openalex publication_date 2016/11/23 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we first establish an L²-type Dolbeault isomorphism for logarithmic differential forms by Hörmander's L²-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of new vanishing theorems for sheaves of logarithmic differential forms on compact Kähler manifolds with simple normal crossing divisors, which generalize several classical vanishing theorems, including Norimatsu's vanishing theorem, Gibrau's vanishing theorem, Le Potier's vanishing theorem and a version of the Kawamata-Viehweg vanishing theorem.

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