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Online ISSN 1534-7486; Print ISSN 1056-3911
Structure theorem, injectivity theorem and vanishing theorem for the cohomology groups of pseudo-effective line bundles
Authors:
Chenghao Qing and Xiangyu Zhou
Journal:
J. Algebraic Geom.
DOI:
https://doi.org/10.1090/jag/853
Published electronically:
June 25, 2025
Full-text PDF
Abstract | References | Additional Information
Abstract: In this paper, we establish a structure theorem and prove an isomorphism theorem for cohomology groups of pseudo-effective line bundles over holomorphically convex manifolds, which generalizes the results of Takegoshi, Demailly-Peternell-Schneider, Meng-Zhou, and Wu. As applications, we first give an answer to a question proposed by Matsumura, and establish an injectivity theorem for purely log terminal pairs generalized to pseudo-effective line bundles with transcendental singularities, and then we obtain a Kollár-Nadel-Ohsawa type vanishing theorem which extends the results of Matsumura, Fujino, Meng-Zhou, and others.
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Additional Information
Chenghao Qing
Affiliation:
Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, People’s Republic of China
Email:
qingchenghao@amss.ac.cn
Xiangyu Zhou
Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
MR Author ID:
260186
Email:
xyzhou@math.ac.cn
Received by editor(s):
October 1, 2024
Received by editor(s) in revised form:
March 31, 2025, and May 14, 2025
Published electronically:
June 25, 2025
Additional Notes:
The second author was supported by National Key R&D Program of China (No. 2021YFA1003100) and NSFC grant (No. 12288201).
Article copyright:
© Copyright 2025
University Press, Inc.