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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共 47 条
  • [21] Fujita K., On Fano threefolds of degree 22 after Cheltsov and Shramov.” Birational Geometry, Kähler–Einstein Metrics and Degenerations, Springer Proceedings in Mathematics & Statistics, 409, pp. 249-262, (2023)
  • [22] Fujita K., Odaka Y., On the K-stability of Fano varieties and anticanonical divisors, Tohoku Math. J, 70, pp. 511-521, (2018)
  • [23] Kishimoto T., Prokhorov Y., Zaidenberg M., G<sub>a</sub>-actions on affine cones, Transform. Groups, 18, pp. 1137-1153, (2013)
  • [24] Green M., Koszul cohomology and the geometry of projective varieties, J. Differential Geom, 19, pp. 125-171, (1984)
  • [25] In-Kyun K., Kim J., Won J., K-unstable sinngular del Pezzo surfaces without anticanonical polar cylinder, (2023)
  • [26] In-Kyun K., Okada T., Won J., Alpha invariants of birationally rigid Fano three-folds, Int. Math. Res. Notices, pp. 2745-2800, (2018)
  • [27] In-Kyun K., Okada T., Won J., Alpha invariants of birationally bi-rigid Fano 3-folds I, Eur. J. Math, 7, pp. 272-308, (2021)
  • [28] In-Kyun K., Okada T., Won J., K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces, Forum Math. Sigma, 11, (2023)
  • [29] In-Kyun K., Viswanathan N., Won J., K-stability of log del Pezzo hypersurfaces with index 2, Int. J. Math, 33, (2022)
  • [30] In-Kyun K., Viswanathan N., Won J., On singular del Pezzo hypersurfaces of index 3, 409, of Springer Proc. Math. Stat, (2023)
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