Compact Kahler manifolds with quasi-positive second Chern-Ricci curvature

被引：0

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：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2024年 / 32卷 / 10期

基金：

国家重点研发计划;

关键词：

HOLOMORPHIC SECTIONAL CURVATURE; SINGULAR HERMITIAN METRICS; PROJECTIVE-MANIFOLDS; RATIONAL CONNECTEDNESS; LINE BUNDLES; VARIETIES; THEOREM; UNIFORMIZATION;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a compact Kahler manifold. We prove that if X admits a smooth Hermitian metric omega with quasi-positive second Chern-Ricci curvature Ric((2))(omega), then X is projective and rationally connected. In particular, X is simply connected.

引用

页码：2717 / 2734

页数：18

共 69 条

[1]

Aronszajn N., 1957, J. Math. Pures Appl, V36, P235

[2] EXISTENCE OF MINIMAL MODELS FOR VARIETIES OF LOG GENERAL TYPE [J].

Birkar, Caucher ;

Cascini, Paolo ;

Hacon, Christopher D. ;

McKernan, James .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 23 (02) :405-468

[3]

Boucksom S, 2013, J ALGEBRAIC GEOM, V22, P201

[4]

Campana F, 2015, LOND MATH S, V417, P71

[5]

CAMPANA F, 1992, ANN SCI ECOLE NORM S, V25, P539

[6] PROJECTIVE-MANIFOLDS WHOSE TANGENT-BUNDLES ARE NUMERICALLY EFFECTIVE [J].

CAMPANA, F ;

PETERNELL, T .

MATHEMATISCHE ANNALEN, 1991, 289 (01) :169-187

[7] A DECOMPOSITION THEOREM FOR PROJECTIVE MANIFOLDS WITH NEF ANTICANONICAL BUNDLE [J].

Cao, Junyan ;

Hoering, Andreas .

JOURNAL OF ALGEBRAIC GEOMETRY, 2019, 28 (03) :567-597

[8] Manifolds with nef anticanonical bundle [J].

Cao, Junyan ;

Horing, Andreas .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2017, 724 :203-244

[9] Rational Curves on Complex Manifolds [J].

Cascini, Paolo .

MILAN JOURNAL OF MATHEMATICS, 2013, 81 (02) :291-315

[10]

Chau A, 2012, J DIFFER GEOM, V92, P187, DOI 10.4310/jdg/1352297805

← 1 2 3 4 5 6 7 →