Extension of cohomology classes and holomorphic sections defined on subvarieties

Zhou, Xiangyu; Zhu, Langfeng

doi:10.1090/jag/766

Authors: Xiangyu Zhou and Langfeng Zhu
Journal: J. Algebraic Geom. 31 (2022), 137-179
DOI: https://doi.org/10.1090/jag/766
Published electronically: September 6, 2021
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Abstract | References | Additional Information

Abstract: In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of quasi-plurisubharmonic functions with arbitrary singularities. The first result gives a positive answer to a question posed by Cao-Demailly-Matsumura and unifies a few well-known injectivity theorems. The second result generalizes and optimizes a general $L^2$ extension theorem obtained by Demailly.

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Additional Information

Xiangyu Zhou
Affiliation: Department of Mathematics, Shanghai University, Shanghai 200444; Institute of Mathematics, Academy of Mathematics and Systems Science, Beijing 100190; and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
MR Author ID: 260186
Email: xyzhou@math.ac.cn

Langfeng Zhu
Affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan 430072, People’s Republic of China
Email: zhulangfeng@amss.ac.cn

Received by editor(s): September 19, 2019
Received by editor(s) in revised form: February 1, 2020
Published electronically: September 6, 2021
Additional Notes: The first author was partially supported by the National Natural Science Foundation of China (No. 11688101 and No. 11431013). The second author was partially supported by the National Natural Science Foundation of China (No. 12022110, No. 11201347, and No. 11671306). Both of the authors are corresponding authors.
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