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arXiv · 1405.5161

Dynamic alpha-invariants of del Pezzo surfaces

Ivan Cheltsov·Jesus Martinez-Garcia
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Abstract

For every smooth del Pezzo surface $S$, smooth curve $C\in|-K_{S}|$ and $β\in(0,1]$, we compute the $α$-invariant of Tian $α(S,(1-β)C)$ and prove the existence of Kähler--Einstein metrics on $S$ with edge singularities along $C$ of angle $2πβ$ for $β$ in certain interval. In particular we give lower bounds for the invariant $R(S,C)$, introduced by Donaldson as the supremum of all $β\in(0,1]$ for which such a metric exists.

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Ivan Cheltsov, Jesus Martinez-Garcia. 2014-05-20. Dynamic alpha-invariants of del Pezzo surfaces. https://doi.org/10.1093/imrn%2Frnv229

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