Endomorphisms of rank one Gorenstein del Pezzo surfaces

TL;DR

This paper classifies Gorenstein del Pezzo surfaces of Picard rank 1 that admit certain endomorphisms, showing they are mostly quotients of toric varieties by specific finite groups, with one exception.

Contribution

It provides a complete classification of Gorenstein del Pezzo surfaces with Picard rank 1 admitting int-amplified endomorphisms, identifying them as quotients of toric varieties.

Findings

Most such surfaces are quotients of toric varieties by finite groups.

The classification includes all such quotients, with one exceptional case.

These surfaces admit int-amplified endomorphisms if and only if they meet the specified conditions.

Abstract

We prove that, in all except one case, a Gorenstein del Pezzo surface of Picard rank 1 admits an int-amplified endomorphism if and only if it is a quotient of a toric variety by a finite group which acts freely in codimension one and preserves the open torus. We classify all such quotients.