Subadditivity of generalized Kodaira dimensions and extension theorems

被引：4

作者：

Zhou, Xiangyu ^{[1
,2
,3
]}

Zhu, Langfeng ^{[4
]}

机构：

[1] Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China

[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[4] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

来源：

INTERNATIONAL JOURNAL OF MATHEMATICS | 2020年 / 31卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Extension theorem; L-2; estimate; multiplier ideal sheaf; Kodaira dimension; Kahler fibration; ALGEBRAIC FIBER SPACES; VARIETIES; CLASSIFICATION; REGULARIZATION; POSITIVITY; CURRENTS; BUNDLES; SHEAVES;

D O I：

10.1142/S0129167X20500986

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce the notion of generalized Kodaira dimension with multiplier ideal sheaves, and prove the subadditivity of these generalized Kodaira dimensions for certain Kahler fibrations, which was originally obtained for Kodaira dimensions of algebraic fiber spaces by Kawamata and Viehweg. Our method is analytic and based on some new results in recent years. The crucial step in our proof is to prove an L-2/k extension theorem for twisted pluricanonical sections on compact Kahler manifolds. Moreover, we also discuss the relation between two previous optimal L-2 extension theorems with singular weights on weakly pseudoconvex Kahler manifolds.

引用

页数：36