Log canonical thresholds on Gorenstein canonical del Pezzo surfaces

TL;DR

This paper classifies effective anticanonical divisors on weak del Pezzo surfaces to determine the minimal log canonical thresholds on Gorenstein canonical del Pezzo surfaces, advancing understanding of their singularity properties.

Contribution

It provides a complete classification of effective anticanonical divisors on weak del Pezzo surfaces and identifies the minimal log canonical thresholds for Gorenstein canonical del Pezzo surfaces.

Findings

Classification of all effective anticanonical divisors on weak del Pezzo surfaces

Determination of the smallest log canonical threshold among these divisors

Enhanced understanding of singularities on Gorenstein canonical del Pezzo surfaces

Abstract

We classify all the effective anticanonical divisors on weak del Pezzo surfaces. Through this classification we obtain the smallest number among the log canonical thresholds of effective anticanonical divisors on a given Gorenstein canonical del Pezzo surface.