RC-positive metrics on rationally connected manifolds

被引：9

作者：

Yang, Xiaokui ^{[1
,2
]}

机构：

[1] Tsinghua Univ, Dept Math, Beijing 100084, Peoples R China

[2] Tsinghua Univ, Yau Math Sci Ctr, Beijing 100084, Peoples R China

来源：

FORUM OF MATHEMATICS SIGMA | 2020年 / 8卷

关键词：

rationally connected; RC-positivity; vanishing theorem; COMPACT KAHLER-MANIFOLDS; PROJECTIVE-MANIFOLDS; VECTOR-BUNDLES; THEOREM; SUBVARIETIES; COHOMOLOGY; VARIETIES; DIMENSION; CONVERSE;

D O I：

10.1017/fms.2020.32

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that if a compact Kahler manifold X has a smooth Hermitian metric omega such that (T-X, omega) is uniformly RC-positive, then X is projective and rationally connected. Conversely, we show that, if a projective manifold X is rationally connected, then there exists a uniformly RC-positive complex Finsler metric on T-X.

引用

页数：19

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