Alpha invariant for general polarization of del Pezzo surfaces of degree 1

TL;DR

This paper establishes a simple numerical criterion to determine K-stability for any ample divisor on smooth del Pezzo surfaces of degree 1, advancing understanding of stability conditions in algebraic geometry.

Contribution

It provides a straightforward numerical condition for K-stability of polarizations on degree 1 del Pezzo surfaces, generalizing previous results.

Findings

Verified K-stability condition for all ample divisors on degree 1 del Pezzo surfaces.

Established a simple numerical criterion for polarization stability.

Contributed to the classification of stable polarizations in algebraic geometry.

Abstract

For an arbitrary ample divisor A in smooth del Pezzo surface S of degree 1, we verify the condition of the polarization (S,A) to be K-stable and it is a simple numerical condition.