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arXiv · 2407.14901

Uniform K-stability of $G$-varieties of complexity 1

Yan Li·Zhenye Li
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Abstract

Let ${\rm k}$ be an algebraically closed field of characteristic 0 and $G$ a connect, reductive group over it. Let $X$ be a projective $G$-variety of complexity 1. We classify $G$-equivariant normal test configurations of $X$ with integral central fibre via the combinatorial data. We also give a formula of anti-canonical divisors on $X$. Based on this formula, when $X$ is $\mathbb Q$-Fano, we give an expression of the Futaki invariant, and derive a criterion of uniform K-stability in terms of the combinatorial data.

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Yan Li, Zhenye Li. 2024-07-20. Uniform K-stability of $G$-varieties of complexity 1. https://arxiv.org/abs/2407.14901

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