, Volume 24, Issue 2, pp 798-842
Date: 11 Oct 2012

Computing α-Invariants of Singular del Pezzo Surfaces

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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 Kähler-Einstein.

Communicated by Gang Tian.
This paper was completed under financial support provided by IKY (Greek State Scholarship Foundation).