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

TY - JOUR

T1 - Compact moduli spaces of Del Pezzo surfaces and Kähler–Einstein metrics

AU - Odaka, Yuji

AU - Spotti, Cristiano

AU - Sun, Song

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84955438491&partnerID=8YFLogxK

M3 - Journal article

SN - 0022-040X

VL - 102

SP - 127

EP - 172

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

IS - 1

ER -