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Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics

We prove that the Gromov-Hausdorff compactification of the moduli space of Kahler-Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tian's theorem on the existence of Kahler-Einstein metrics on smooth Del Pezzo surfaces and classifies the degenerations of such metrics. The proof is based on a combination of both algebraic and differential geometric techniques.

preprint2015arXivOpen access
Yuji OdakaCristiano SpottiSong Sun
math.AGmath.DG
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Yuji OdakaCristiano SpottiSong Sun

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