G-birational superrigidity of del Pezzo surfaces of degree 2 and 3

TL;DR

This paper classifies G-birationally superrigid del Pezzo surfaces of degree 2 and 3, identifying which are superrigid and describing automorphism groups for the others.

Contribution

It provides a classification of G-birationally superrigid del Pezzo surfaces of degrees 2 and 3, and details the automorphism groups for non-superrigid cases.

Findings

Del Pezzo surfaces of degree < 3 are G-birationally rigid.

Classification of G-birationally superrigid surfaces of degree 2 and 3.

Explicit descriptions of automorphism groups for non-superrigid cases.

Abstract

Any minimal Del Pezzo G-surface S of degree smaller than 3 is G-birationally rigid. We classify those which are G-birationally superrigid and for those which fail to be so, we describe the equations of a set of generators for the infinite group of G-birational automorphisms.