Del Pezzo surfaces with 1/3(1,1) points

TL;DR

This paper classifies del Pezzo surfaces with specific quotient singularities, details their deformation families, invariants, and models, and identifies which can degenerate to toric surfaces, advancing mirror symmetry studies for orbifold del Pezzo surfaces.

Contribution

It provides a comprehensive classification, explicit models, and degeneration results for del Pezzo surfaces with 1/3(1,1) points, linking to mirror symmetry research.

Findings

29 qG-deformation families classified

26 families admit qG-degenerations to toric surfaces

Explicit models as degeneracy loci in quotient varieties

Abstract

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.