Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics
Differential Geometry
2015-03-11 v3 Algebraic Geometry
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 the degenerations of such metrics. The proof is based on a combination of both algebraic and differential geometric techniques.
Keywords
Cite
@article{arxiv.1210.0858,
title = {Compact Moduli Spaces of Del Pezzo Surfaces and K\"ahler-Einstein metrics},
author = {Yuji Odaka and Cristiano Spotti and Song Sun},
journal= {arXiv preprint arXiv:1210.0858},
year = {2015}
}
Comments
Final version. To appear in J. Diff. Geom