Equivariant \mathbb R-test configurations of polarized spherical varieties

2022/06/10 by Yan Li, Li, Yan, Zhenye Li +1
Mathematics · #Advanced Algebra and Geometry #Geometry and complex manifolds #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2206.04880

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.

Related

• Equivariant \mathbb R-test configurations and semistable limits of \mathbb Q-Fano group compactifications
• Weighted K-stability of \mathbb Q-Fano spherical varieties
• K-stability and polystable degenerations of polarized spherical varieties
• Existence of equivariant models of spherical varieties and other G-varieties
• Stable spherical varieties and their moduli