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arXiv · 2405.06883

Asymptotic Chow stability of uniformly K-stable toric varieties

King leung Lee·Naoto Yotsutani
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Abstract

For a polarized toric variety, we provide a sufficient criterion ensuring that a uniformly K-stable polarized toric variety $(X,L)$ is asymptotically Chow polystable, under the assumption that the obstruction to asymptotic Chow semistability (the Futaki-Ono invariant) vanishes. Our approach is based on a detailed study of triangulations of neighborhoods of the vertices of the associated moment polytope $\Delta$. As an application, we prove that every uniformly K-stable polarized smooth toric variety $(X,L)$ with vanishing Futaki-Ono invariant is asymptotically Chow polystable.

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King leung Lee, Naoto Yotsutani. 2024-05-11. Asymptotic Chow stability of uniformly K-stable toric varieties. https://arxiv.org/abs/2405.06883

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