Local delta invariants of weak del Pezzo surfaces with the anti-canonical degree $\geq 5$

TL;DR

This paper computes the local delta invariants for all weak del Pezzo surfaces with anti-canonical degree at least 5, providing insights into their K-stability properties.

Contribution

It provides a complete determination of local delta invariants for a class of weak del Pezzo surfaces, advancing understanding of their stability criteria.

Findings

Calculated local delta invariants for all relevant weak del Pezzo surfaces.

Established criteria linking delta invariants to K-stability.

Enhanced classification of weak del Pezzo surfaces based on stability.

Abstract

The delta invariant interprets the criterion for the K-(poly)stability of log terminal Fano varieties. In this paper, we determine the whole local delta invariant for all weak del Pezzo surfaces with the anti-canonical degree $\geq 5$.