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

被引：22
|
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
收藏
页码：177 / 204
页数：28
相关论文
共 50 条
  • [1] SESHADRI CONSTANTS AND K-STABILITY OF FANO MANIFOLDS
    Abban, Hamid
    Zhuang, Ziquan
    DUKE MATHEMATICAL JOURNAL, 2023, 172 (06) : 1109 - 1144
  • [2] K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS
    Fujita, Kento
    JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2019, 18 (03) : 519 - 530
  • [3] Relative Ding and K-stability of toric Fano manifolds in low dimensions
    Yasufumi Nitta
    Shunsuke Saito
    Naoto Yotsutani
    European Journal of Mathematics, 2023, 9
  • [4] ON FANO VARIETIES WITH TORUS ACTION OF COMPLEXITY 1
    Herppich, Elaine
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2014, 57 (03) : 737 - 753
  • [5] Relative Ding and K-stability of toric Fano manifolds in low dimensions
    Nitta, Yasufumi
    Saito, Shunsuke
    Yotsutani, Naoto
    EUROPEAN JOURNAL OF MATHEMATICS, 2023, 9 (02)
  • [6] K-stability on toric manifolds
    Zhou, Bin
    Zhu, Xiaohua
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (09) : 3301 - 3307
  • [7] K-stability for Kahler manifolds
    Dervan, Ruadhai
    Ross, Julius
    MATHEMATICAL RESEARCH LETTERS, 2017, 24 (03) : 689 - 739
  • [8] Birational Superrigidity and K-Stability of Projectively Normal Fano Manifolds of Index One
    Suzuki, Fumiaki
    MICHIGAN MATHEMATICAL JOURNAL, 2021, 70 (04) : 779 - 792
  • [9] On K-stability of Fano weighted hypersurfaces
    Sano, Taro
    Tasin, Luca
    ALGEBRAIC GEOMETRY, 2024, 11 (02): : 296 - 317
  • [10] K-STABILITY OF FANO SPHERICAL VARIETIES
    Delcroix, Thibaut
    ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2020, 53 (03): : 615 - 662
12345