K-polystability of the first secant varieties of rational normal curves

In-Kyun Kim; Jinhyung Park; Joonyeong Won

K-polystability of the first secant varieties of rational normal curves

Algebraic Geometry 2023-11-23 v1

Authors: In-Kyun Kim , Jinhyung Park , Joonyeong Won

Abstract

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

Keywords

rational normal curve first secant variety k-polystability q-fano threefold weak kahler-einstein metric polar cylinder

Cite

@article{arxiv.2311.13115,
  title  = {K-polystability of the first secant varieties of rational normal curves},
  author = {In-Kyun Kim and Jinhyung Park and Joonyeong Won},
  journal= {arXiv preprint arXiv:2311.13115},
  year   = {2023}
}

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17 pages

K-polystability of the first secant varieties of rational normal curves

Abstract

Keywords

Cite

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