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arXiv · 1611.07671

Logarithmic vanishing theorems on compact Kähler manifolds I

Chunle Huang·Kefeng Liu·Xueyuan Wan·Xiaokui Yang
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Abstract

In this paper, we first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by Hörmander's $L^2$-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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Chunle Huang, Kefeng Liu, Xueyuan Wan, Xiaokui Yang. 2016-11-23. Logarithmic vanishing theorems on compact Kähler manifolds I. https://arxiv.org/abs/1611.07671

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