Stable polarized del Pezzo surfaces

TL;DR

This paper provides a straightforward criterion to determine K-stability of polarized del Pezzo surfaces, which ensures the existence of constant scalar curvature Kähler metrics in the associated polarization class.

Contribution

It introduces a simple sufficient condition for K-stability and the existence of special metrics on polarized del Pezzo surfaces, advancing understanding in complex differential geometry.

Findings

Established a new criterion for K-stability of del Pezzo surfaces.

Linked K-stability to the existence of constant scalar curvature Kähler metrics.

Simplified the conditions needed for stability and metric existence.

Abstract

We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization.