Del Pezzo Surfaces in Weighted Projective Spaces

TL;DR

This paper classifies all quasi-smooth, well-formed singular del Pezzo surfaces that are weighted hypersurfaces using a new algorithm, advancing understanding of their structure in algebraic geometry.

Contribution

It introduces an algorithm to classify all such del Pezzo surfaces in weighted projective spaces, a novel approach in the field.

Findings

Complete classification of quasi-smooth, well-formed singular del Pezzo surfaces in weighted hypersurfaces

Development of an algorithm for systematic classification

Enhanced understanding of the structure of these surfaces

Abstract

We study singular del Pezzo surfaces that are quasi-smooth and well-formed weighted hypersurfaces. We give an algorithm how to classify all of them.