Extension of cohomology classes and holomorphic sections defined on subvarieties

2019/09/19 by Zhou, Xiangyu, Zhu, Langfeng · 1 citation
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.08822

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 L² extension theorem obtained by Demailly.

Cited by

• L² extension of holomorphic functions and log canonical places

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