Birational geometry of actions on del Pezzo surfaces

TL;DR

This paper classifies finite group actions on del Pezzo surfaces up to birational equivalence, resolving open problems in equivariant birational geometry and identifying birationally rigid actions.

Contribution

It completes the classification of regular generically free actions of finite groups on del Pezzo surfaces and addresses open questions in the field.

Findings

Classified all regular generically free finite group actions on del Pezzo surfaces.

Settled several open problems in equivariant birational geometry.

Identified and classified birationally rigid actions on del Pezzo surfaces.

Abstract

We complete the classification of regular generically free actions of finite groups on del Pezzo surfaces, up to birational equivalence. As a byproduct, we settle several open problems in equivariant birational geometry, e.g., we classify birationally rigid actions on del Pezzo surfaces.