G-coregularity of del Pezzo surfaces

TL;DR

This paper introduces the concept of G-coregularity for algebraic varieties with finite group actions, computes it for certain del Pezzo surfaces, and explores its relations with other invariants and group actions.

Contribution

It defines G-coregularity, computes it for smooth del Pezzo surfaces of degree ≥6, and characterizes groups acting on conic bundles with G-coregularity 0.

Findings

G-coregularity computed for smooth del Pezzo surfaces of degree ≥6

Characterization of groups acting on conic bundles with G-coregularity 0

Relations established between G-coregularity, G-log-canonical thresholds, G-rigidity, and quotient singularities

Abstract

We introduce and study the notion of $G$-coregularity of algebraic varieties endowed with an action of a finite group $G$. We compute $G$-coregularity of smooth del Pezzo surfaces of degree at least 6, and give a characterization of groups that can act on conic bundles with $G$-coregularity 0. We describe the relations between the notions of $G$-coregularity, $G$-log-canonical thresholds, $G$-rigidity, and exceptional quotient singularities.