# Computing $α$-invariants of singular del Pezzo surfaces - Mathematics > Algebraic Geometry

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Abstract: We prove new local inequality for divisors on surfaces and utilize it tocompute $\alpha$-invariants of singular del Pezzo surfaces, which implies thatdel 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 K\-ahler-Einstein.

Autor: Ivan Cheltsov, Dimitra Kosta

Fuente: https://arxiv.org/