Delta invariants of singular del Pezzo surfaces

TL;DR

This paper estimates delta-invariants of certain singular del Pezzo surfaces with quotient singularities and demonstrates that these surfaces admit orbifold Kähler–Einstein metrics, extending previous work from ten years ago.

Contribution

It provides new estimates of delta-invariants for specific singular del Pezzo surfaces and confirms the existence of orbifold Kähler–Einstein metrics on them.

Findings

Each studied surface admits an orbifold Kähler–Einstein metric.

Delta-invariants are explicitly estimated for these singular surfaces.

The results extend previous estimates from ten years ago.

Abstract

We estimate $\delta$-invariants of some singular del Pezzo surfaces with quotient singularities, which we studied ten years ago. As a result, we show that each of these surfaces admits an orbifold K\"ahler--Einstein metric.