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Computing $α$-invariants of singular del Pezzo surfaces (1010.0043v3)
Published 1 Oct 2010 in math.AG and math.DG
Abstract: We prove new local inequality for divisors on surfaces and utilize it to compute $\alpha$-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 K\"ahler-Einstein.
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