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

Yuji Odaka, Cristiano Spotti, Song Sun

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

71 Citations (Scopus)

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.

Original languageEnglish
JournalJournal of Differential Geometry
Volume102
Issue1
Pages (from-to)127-172
Number of pages46
ISSN0022-040X
Publication statusPublished - Jan 2016
Externally publishedYes

Fingerprint

Dive into the research topics of 'Compact moduli spaces of Del Pezzo surfaces and Kähler–Einstein metrics'. Together they form a unique fingerprint.

Cite this