Classification of Toric log Del Pezzo Surfaces having Picard Number 1 and Index $\le 3$

TL;DR

This paper extends the classification of toric log Del Pezzo surfaces with Picard number 1 to include those with index 3, establishing that exactly 18 such surfaces exist up to isomorphism.

Contribution

The paper provides a complete classification of toric log Del Pezzo surfaces with Picard number 1 and index 3, expanding previous classifications for lower indices.

Findings

Exactly 18 such surfaces exist up to isomorphism

Classification extends previous work for index ≤ 2

Provides explicit characterization of these surfaces

Abstract

Toric log Del Pezzo surfaces with Picard number 1 have been completely classified whenever their index is $\le 2$: In this paper we extend the classification for those having index 3: We prove that, up to isomorphism, there are exactly 18 surfaces of this kind.