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- Title
Vanishing Theorems for Sheaves of Logarithmic Differential Forms on Compact Kähler Manifolds.
- Authors
Huang, Chunle; Liu, Kefeng; Wan, Xueyuan; Yang, Xiaokui
- Abstract
In this paper, we first establish an |$L^2$| -type Dolbeault isomorphism for logarithmic differential forms by Hrmander'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, Girbau's vanishing theorem, Le Potier's vanishing theorem, and a version of the Kawamata–Viehweg vanishing theorem.
- Subjects
VANISHING theorems; DIFFERENTIAL forms; SHEAF theory; ISOMORPHISM (Mathematics)
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 16, p13501
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnac204