Logarithmic vanishing theorems on compact K\"{a}hler manifolds I
Algebraic Geometry
2016-11-24 v1 Complex Variables
Abstract
In this paper, we first establish an -type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's -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 K\"ahler 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.
Cite
@article{arxiv.1611.07671,
title = {Logarithmic vanishing theorems on compact K\"{a}hler manifolds I},
author = {Chunle Huang and Kefeng Liu and Xueyuan Wan and Xiaokui Yang},
journal= {arXiv preprint arXiv:1611.07671},
year = {2016}
}