Equivariant unirationality of del Pezzo surfaces of degree 3 and 4

TL;DR

This paper investigates the conditions under which complex del Pezzo surfaces of degree 3 and 4 are G-unirational, extending the classical concept of unirationality to include group actions.

Contribution

It provides a comprehensive classification of G-unirationality for del Pezzo surfaces of degree 3 and 4, generalizing previous results to equivariant settings.

Findings

Characterizes G-unirationality for degree 3 and 4 del Pezzo surfaces.

Establishes criteria for the existence of G-equivariant dominant rational maps.

Extends the notion of unirationality to equivariant contexts for these surfaces.

Abstract

A variety X with an action of a finite group G is said to be G-unirational if there is a G-equivariant dominant rational map V -> X where V is a faithful linear representation of G. This generalizes the usual notion of unirationality. We determine when X is G-unirational for any complex del Pezzo surface X of degree at least 3.