Classification of low degree del Pezzo orbifolds

TL;DR

This paper classifies low degree del Pezzo orbifolds with irreducible boundaries by analyzing low degree curves on del Pezzo surfaces, using classical algebraic geometry tools.

Contribution

It provides a new classification of low degree del Pezzo orbifolds with irreducible boundaries, expanding understanding of Campana orbifolds.

Findings

Classification of low degree del Pezzo orbifolds achieved

Identification of specific low degree curves on del Pezzo surfaces

Application of classical theorems in the classification process

Abstract

In this paper we classify low degree del Pezzo orbifolds with irreducible boundaries. In order to achieve desired boundaries, we classify low degree curves on low degree del Pezzo surfaces. The notion of Campana orbifolds was introduced by Campana in 2004. A del Pezzo orbifold is a Campana orbifold whose underlying surface is a del Pezzo surface. The classification is elementary applications of adjunction formula, Riemann-Roch theorem, Hodge Index theorem and Kawamata-Viehweg vanishing theorem.