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

Yuji Odaka, Cristiano Spotti, Song Sun

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Abstract

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.

OriginalsprogEngelsk
TidsskriftJournal of Differential Geometry
Vol/bind102
Nummer1
Sider (fra-til)127-172
Antal sider46
ISSN0022-040X
StatusUdgivet - 2016
Udgivet eksterntJa

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