Uniqueness of K-polystable degenerations of Fano varieties

被引：47

作者：

Blum, Harold ^{[1
]}

Xu, Chenyang ^{[2
,3
]}

机构：

[1] Univ Utah, Salt Lake City, UT 84112 USA

[2] Beijing Int Ctr Math Res, Beijing, Peoples R China

[3] MIT, 77 Massachusetts Ave, Cambridge, MA 02139 USA

来源：

ANNALS OF MATHEMATICS | 2019年 / 190卷 / 02期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Fano varieties; K-stability; degenerations; moduli; KAHLER-EINSTEIN METRICS; MODULI SPACES; SCALAR CURVATURE; STABILITY; EXISTENCE; VOLUME; VALUATIONS;

D O I：

10.4007/annals.2019.190.2.4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that K-polystable degenerations of Q-Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable Q-Fano varieties is separated. Together with recently proven boundedness and openness statements, the latter result yields a separated Deligne-Mumford stack parametrizing all uniformly K-stable Q-Fano varieties of fixed dimension and volume. The result also implies that the automorphism group of a K-stable Q-Fano variety is finite.

引用

页码：609 / 656

页数：48

共 60 条

[1]

Abramovich D, 2010, EMS SER CONGR REP, P1

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