Normal del Pezzo surfaces containing a nonrational singularity

TL;DR

This paper classifies certain normal del Pezzo surfaces with specific singularities over perfect fields, revealing an infinite hierarchy and providing insights into their anticanonical models.

Contribution

It introduces a classification of normal del Pezzo surfaces with nonrational singularities and describes their hierarchical structure and transformations.

Findings

Identification of an infinite hierarchy of such surfaces

Description of contractions of ruled surfaces within this hierarchy

Determination of 2D anticanonical models for normal surfaces

Abstract

Working over a perfect field, I classify normal del Pezzo surfaces with base number one that contain a nonrational singularity. They form a huge infinite hierarchy; contractions of ruled surfaces lie on top of it. Descending the hierarchy hinges on a generalized version of elementary transformations. As an application, I determine the structure of 2-dimensional anticanonical models for arbitrary normal surfaces.