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Compact moduli spaces of Del Pezzo surfaces and KhlerEinstein metrics

Yuji Odaka Cristiano Spotti SONG SUN

Differential Geometry mathscidoc:1912.43453

Journal of Differential Geometry, 102, (1), 127-172, 2016
We prove that the GromovHausdorff compactification of the moduli space of KhlerEinstein Del Pezzo surfaces in each degree agrees with certain algebro-geometric compactification. In particular, this recovers Tians theorem on the existence of KhlerEinstein 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.
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@inproceedings{yuji2016compact,
  title={Compact moduli spaces of Del Pezzo surfaces and KhlerEinstein metrics},
  author={Yuji Odaka, Cristiano Spotti, and SONG SUN},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114530822980013},
  booktitle={Journal of Differential Geometry},
  volume={102},
  number={1},
  pages={127-172},
  year={2016},
}
Yuji Odaka, Cristiano Spotti, and SONG SUN. Compact moduli spaces of Del Pezzo surfaces and KhlerEinstein metrics. 2016. Vol. 102. In Journal of Differential Geometry. pp.127-172. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221114530822980013.
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