On a conjecture of Hong and Won

TL;DR

This paper provides a specific counter-example to disprove a conjecture regarding the alpha-invariants of polarized smooth del Pezzo surfaces of degree one.

Contribution

It presents an explicit counter-example that challenges the previously conjectured property of alpha-invariants in this class of surfaces.

Findings

Counter-example disproves the conjecture.

Clarifies the behavior of alpha-invariants in degree one del Pezzo surfaces.

Contributes to the understanding of stability conditions in algebraic geometry.

Abstract

We give an explicit counter-example to a conjecture of Kyusik Hong and Joonyeong Won about $\alpha$-invariants of polarized smooth del Pezzo surfaces of degree one.