Delta-invariants for Fano varieties with large automorphism groups

Abstract

For a variety $X$, a big $\mathbb{Q}$-divisor $L$ and a closed connected subgroup $G\subset \mathrm{Aut}(X,L)$ we define a $G$-invariant version of the $\delta$-threshold. We prove that for a Fano variety $(X,-K_X)$ and a connected subgroup $G\subset \mathrm{Aut}(X)$ this invariant characterizes $G$-equivariant uniform $K$-stability. We also use this invariant to investigate $G$-equivariant $K$-stability of some Fano varieties with large groups of symmetries, including spherical Fano varieties. We also consider the case of $G$ being a finite group.

arXiv commentfinal version, to appear in IJM

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Cited by in corpus (5)

• Basis divisors and balanced metrics
• K-stability of Gorenstein Fano group compactifications with rank two
• G-coregularity of del Pezzo surfaces
• Kähler-Einstein metrics on smooth Fano toroidal symmetric varieties of type AIII
• Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one