Open AccessExtension of cohomology classes and holomorphic sections defined on subvarieties
Author(s) -
Xiangyu Zhou,
Langfeng Zhu
Publication year - 2021
Publication title -
journal of algebraic geometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.824
H-Index - 50
eISSN - 1534-7486
pISSN - 1056-3911
DOI - 10.1090/jag/766
Subject(s) - holomorphic function , mathematics , cohomology , extension (predicate logic) , pure mathematics , sheaf , quotient , algebra over a field , computer science , programming language
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 L^2 extension theorem obtained by Demailly.