K-STABILITY FOR FANO MANIFOLDS WITH TORUS ACTION OF COMPLEXITY 1

被引：27

作者：

Ilten, Nathan ^{[1
]}

Suss, Hendrik ^{[2
]}

机构：

[1] Simor Fraser Univ, Dept Math, Burnaby, BC, Canada

[2] Univ Manchester, Sch Math, Manchester, Lancs, England

来源：

DUKE MATHEMATICAL JOURNAL | 2017年 / 166卷 / 01期

关键词：

KAHLER-EINSTEIN METRICS; T-VARIETIES; RICCI SOLITONS; INVARIANT; SINGULARITIES; DIVISORS; LIMITS; 2-PI;

D O I：

10.1215/00127094-3714864

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider Fano manifolds admitting an algebraic torus action with general orbit of codimension 1. Using a recent result of Datar and Szekelyhidi, we effectively determine the existence of Kahler-Ricci solitons for those manifolds via the notion of equivariant K-stability. This allows us to give new examples of Kahler-Einstein Fano threefolds and Fano threefolds admitting a nontrivial Kahler-Ricci soliton.

引用

页码：177 / 204

页数：28

共 25 条

[1] Polyhedral divisors and algebraic torus actions [J].

Altmann, K ;

Hausen, J .

MATHEMATISCHE ANNALEN, 2006, 334 (03) :557-607

[2] Gluing affine torus actions via divisorial fans [J].

Altmann, Klaus ;

Hausen, Juergen ;

Suess, Hendrik .

TRANSFORMATION GROUPS, 2008, 13 (02) :215-242

[3]

Altmann K, 2012, EMS SER CONGR REP, P17

[4]

BERMAN R. J., ARXIV14018264V1MATHD

[5]

Chen XX, 2015, J AM MATH SOC, V28, P235

[6]

Chen XX, 2015, J AM MATH SOC, V28, P199

[7]

Chen XX, 2015, J AM MATH SOC, V28, P183

[8] Kahler-Einstein Metrics and Stability [J].

Chen, Xiuxiong ;

Donaldson, Simon ;

Sun, Song .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014, 2014 (08) :2119-2125

[9]

DATAR V., 2016, GEOM FUNCT ANAL

[10]

Hartshorne R., 1977, Graduate Texts in Mathematics, V52

← 1 2 3 →