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Compact moduli spaces of Del Pezzo surfaces and Kähler–Einstein metrics

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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 all the degenerations of such metrics. The proof is based on a combination of both algebraic and differential geometric techniques.

Original languageEnglish
JournalJournal of Differential Geometry
Pages (from-to)127-172
Number of pages46
Publication statusPublished - 2016
Externally publishedYes

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