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arXiv · 2601.00054

K-stability of Q-Fano Spherical Varieties via Compatible Divisors

Renpeng Zheng
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Abstract

We study the K-stability of $\mathbb{Q}$-Fano spherical varieties using compatible divisors. More precisely, if the $\mathbb{Q}$-Fano variety, with a reductive group action, has an open Borel subgroup orbit, then there is a unique anticanonical $\mathbb{Q}$-divisor computing the equivariant stability threshold. This $\mathbb{Q}$-divisor is invariant under the Borel subgroup action, and it characterizes the K-stability of a $\mathbb{Q}$-Fano spherical variety.

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Renpeng Zheng. 2025-12-31. K-stability of Q-Fano Spherical Varieties via Compatible Divisors. https://arxiv.org/abs/2601.00054

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