On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties

Chi Li, Xiaowei Wang, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


In this paper we investigate the geometry of the orbit space of the closure of the subscheme parameterizing smooth Kähler-Einstein Fano manifolds inside an appropriate Hilbert scheme. In particular, we prove that being K-semistable is a Zariski-open condition, and we establish the uniqueness of the Gromov-Hausdorff limit for a punctured flat family of Kähler-Einstein Fano manifolds. Based on these, we construct a proper scheme parameterizing the S-equivalent classes of Q-Gorenstein smoothable, K-semistable Q-Fano varieties, and we verify various necessary properties to guarantee that it is a good moduli space.

Original languageEnglish (US)
Pages (from-to)1387-1459
Number of pages73
JournalDuke Mathematical Journal
Issue number8
StatePublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'On the proper moduli spaces of smoothable Kähler-Einstein Fano varieties'. Together they form a unique fingerprint.

Cite this