Computing α-Invariants of Singular del Pezzo Surfaces

Abstract

We prove a new local inequality for divisors on surfaces and utilize it to compute α-invariants of singular del Pezzo surfaces, which implies that del Pezzo surfaces of degree one whose singular points are of type \(\mathbb{A}_{1}\), \(\mathbb{A}_{2}\), \(\mathbb{A}_{3}\), \(\mathbb{A}_{4}\), \(\mathbb{A}_{5}\), or \(\mathbb{A}_{6}\) are Kahler-Einstein.