Classification of log smooth toric del Pezzo pairs

TL;DR

This paper classifies all log-Fano pairs consisting of smooth toric surfaces and equivariant divisors with simple normal crossings, providing a comprehensive description of such pairs.

Contribution

It offers a complete classification of log-Fano pairs for smooth toric surfaces with equivariant divisors, expanding understanding of their geometric structure.

Findings

Provides explicit descriptions of all such pairs.

Characterizes the conditions for log-Fano property.

Enhances classification theory of toric pairs.

Abstract

We give a description of all log-Fano pairs (X, D) where X is a smooth toric surface and D a reduced simple normal crossing divisor such that the pair (X, D) is equivariant.