Equivariant \mathbb R-test configurations and semistable limits of \mathbb Q-Fano group compactifications

2021/03/11 by Li, Yan, Li, ZhenYe
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.06439

Abstract

Let G be a connected, complex reductive group. In this paper, we classify G× G-equivariant normal \mathbb R-test configurations of a polarized G-compactification. Then for \mathbb Q-Fano G-compactifications, we express the H-invariant of its equivariant normal \mathbb R-test configurations in terms of the combinatory data. Based on \citeHan-Li, we compute the semistable limit of a K-unstable Fano G-compactification. As an application, we show that for the two K-unstable Fano SO₄(\mathbb C)-compactifications, the corresponding semistable limits are indeed the limit spaces of the normalized Kähler-Ricci flow.

Related

• Weighted K-stability of \mathbb Q-Fano spherical varieties
• Equivariant \mathbb R-test configurations of polarized spherical varieties
• A technical remark on the Donaldson-Futaki invariant for Fano reductive group compactifications
• Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties
• Uniform K-stability of G-varieties of complexity 1