K-polystability of the First Secant Varieties of Rational Normal Curves

被引：0
作者：
Kim, In-Kyun [1 ]
Park, Jinhyung [2 ]
Won, Joonyeong [3 ]
机构：
[1] KIAS, June E Huh Ctr Math Challenges, 85 Hoegiro Dongdaemun Gu, Seoul 02455, South Korea
[2] Korea Adv Inst Sci & Technol, Dept Math Sci, 291 Daehak-ro, Daejeon 34141, South Korea
[3] Ewha Womans Univ, Dept Math, 52 Ewhayeodae gil, Seoul 03760, South Korea
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2025年 / 2025卷 / 07期
基金：
新加坡国家研究基金会;
关键词：
KAHLER-EINSTEIN METRICS; FANO VARIETIES; SYZYGY CONJECTURE; STABILITY;
D O I：
10.1093/imrn/rnaf088
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The first secant variety $\Sigma $ of a rational normal curve of degree $d \geq 3$ is known to be a $\textbf{Q}$-Fano threefold. In this paper, we prove that $\Sigma $ is K-polystable, and hence, $\Sigma $ admits a weak K & auml;hler-Einstein metric. We also show that there exists a $(-K_{\Sigma })$-polar cylinder in $\Sigma $.
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页数：17
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