@article{c2ccf28e2ea84c5a9eee502692db40ec,
title = "Quasi-projectivity of the moduli space of smooth k{\"a}hler-Einstein fano manifolds",
abstract = "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 K{\"a}hler-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 K{\"a}hler-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.",
author = "Chi Li and Xiaowei Wang and Chenyang Xu",
note = "Funding Information: A. – The first author would like to thank Robert Berman for bringing the related question of continuity for Ding energy to his attention, and Laszlo Lempert for discussion related to Proposition 2.5. We would like to thank Gang Tian for useful comments on the history of CM line bundles. We would also like to thank Dan Abramovich, Aise Johan de Jong, Mircea Mustat,a˘, Julius Ross for very helpful discussions and comments and the referee for clarifying suggestions. The first author is partially supported by NSF: DMS-1405936. The second author is partially supported by a Collaboration Grants for Mathematicians from Simons Foundation: 281299 and NSF:DMS-1609335. The third author is partially supported by the grant “The National Science Fund for Distinguished Young Scholars (11425101)”. The authors would like to thank Samy Tindel for translating the abstract into French. Publisher Copyright: {\textcopyright} 2018 Soci{\'e}t{\'e} Math{\'e}matique de France. Tous droits r{\'e}serv{\'e}s.",
year = "2018",
month = may,
day = "1",
doi = "10.24033/asens.2365",
language = "English (US)",
volume = "51",
pages = "739--772",
journal = "Annales Scientifiques de l'Ecole Normale Superieure",
issn = "0012-9593",
publisher = "Societe Mathematique de France",
number = "3",
}