Unstable polarized del Pezzo surfaces

TL;DR

This paper introduces new examples of K-unstable polarized del Pezzo surfaces using modified test configurations, providing obstructions to the existence of constant scalar curvature Kähler metrics on these surfaces.

Contribution

It presents novel K-unstability examples for polarized del Pezzo surfaces via flopped test configurations, advancing understanding of their geometric stability.

Findings

New K-unstability examples for del Pezzo surfaces

Obstructions to constant scalar curvature Kähler metrics

Application of flopped test configurations

Abstract

We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide new obstructions for the existence of constant scalar curvature Kahler metrics on polarized smooth del Pezzo surfaces.