Endomorphisms of rank one Gorenstein del Pezzo surfaces

2025/12/03 by Joshi, Rohan · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.03527

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.

Citations

• Endomorphisms of varieties and Bott vanishing
• Intersection theory and Chern classes on normal varieties
• Del Pezzo surfaces with infinite automorphism groups
• On rank one log del Pezzo surfaces in characteristic different from two and three
• Building blocks of amplified endomorphisms of normal projective varieties
• Building blocks of amplified endomorphisms of normal projective varieties
• Questions on self maps of algebraic varieties
• On Gorenstein Surfaces Dominated by P²
• On Gorenstein log del Pezzo Surfaces

Cited by

• Endomorphisms of singular del Pezzo surfaces

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• Endomorphisms of singular del Pezzo surfaces
• Int-amplified endomorphisms on normal projective surfaces
• Equivariant classification of Gorenstein open log del Pezzo surfaces with finite group actions
• On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms