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arXiv · 2311.13115

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

In-Kyun Kim·Jinhyung Park·Joonyeong Won
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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 $\Sigma$.

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In-Kyun Kim, Jinhyung Park, Joonyeong Won. 2023-11-22. K-polystability of the first secant varieties of rational normal curves. https://arxiv.org/abs/2311.13115

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