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

In Kyun Kim; Jinhyung Park; Joonyeong Won

doi:10.1093/imrn/rnaf088

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

In Kyun Kim
, Jinhyung Park
, Joonyeong Won

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The first secant variety Σ of a rational normal curve of degree d ≥ 3 is known to be a Q-Fano threefold. In this paper, we prove that Σ is K-polystable, and hence, Σ admits a weak Kähler–Einstein metric. We also show that there exists a (-K_Σ)-polar cylinder in Σ.

Original language	English
Article number	rnaf088
Journal	International Mathematics Research Notices
Volume	2025
Issue number	7
DOIs	https://doi.org/10.1093/imrn/rnaf088
State	Published - 1 Apr 2025

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© The Author(s) 2025. Published by Oxford University Press. All rights reserved.

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title = "K-polystability of the First Secant Varieties of Rational Normal Curves",

abstract = "The first secant variety Σ of a rational normal curve of degree d ≥ 3 is known to be a Q-Fano threefold. In this paper, we prove that Σ is K-polystable, and hence, Σ admits a weak K{\"a}hler–Einstein metric. We also show that there exists a (-KΣ)-polar cylinder in Σ.",

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AB - The first secant variety Σ of a rational normal curve of degree d ≥ 3 is known to be a Q-Fano threefold. In this paper, we prove that Σ is K-polystable, and hence, Σ admits a weak Kähler–Einstein metric. We also show that there exists a (-KΣ)-polar cylinder in Σ.

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

Abstract

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