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arXiv · 2206.04880

Equivariant $\mathbb R$-test configurations of polarized spherical varieties

Yan Li·Zhenye Li
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Abstract

Let $G$ be a connected, complex reductive Lie group and $G/H$ a spherical homogenous space. Let $(X,L)$ be a polarized $G$-variety which is a spherical embedding of $G/H$. In this paper we classify $G$-equivariant normal $\mathbb R$-test configurations of $(X,L)$ via combinatory data. In particular we classify the special ones, and prove a finiteness theorem of central fibres of $G$-equivariant special $\mathbb R$-test configurations. Also, as an application we study the semistable degeneration problem of a $\mathbb Q$-Fano spherical variety.

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Yan Li, Zhenye Li. 2022-06-10. Equivariant $\mathbb R$-test configurations of polarized spherical varieties. https://arxiv.org/abs/2206.04880

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