Journal of Differential Geometry

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

Yuji Odaka, Cristiano Spotti, and Song Sun

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Abstract

We prove that the Gromov–Hausdorff compactification of the moduli space of Kähler–Einstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tian’s theorem on the existence of Kähler–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.

Article information

Source
J. Differential Geom., Volume 102, Number 1 (2016), 127-172.

Dates
First available in Project Euclid: 5 January 2016

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1452002879

Digital Object Identifier
doi:10.4310/jdg/1452002879

Mathematical Reviews number (MathSciNet)
MR3447088

Zentralblatt MATH identifier
1344.58008

Citation

Odaka, Yuji; Spotti, Cristiano; Sun, Song. Compact moduli spaces of Del Pezzo surfaces and Kähler–Einstein metrics. J. Differential Geom. 102 (2016), no. 1, 127--172. doi:10.4310/jdg/1452002879. https://projecteuclid.org/euclid.jdg/1452002879


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