Quasi-projectivity of the moduli space of smooth kähler-Einstein fano manifolds

Chi Li, Xiaowei Wang, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


In this paper, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space M of smoothable Kähler-Einstein Fano varieties. The Chern curvature of this Hermitian metric is the Weil-Petersson current, which exists as a closed positive (1,1)-current on M and extends the canonical Weil-Petersson current on the moduli space M of smooth Kähler-Einstein Fano manifolds. As a consequence, we show that the CM line bundle is nef and big on M and its restriction on M is ample.

Original languageEnglish (US)
Pages (from-to)739-772
Number of pages34
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Issue number3
StatePublished - May 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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