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 language||English (US)|
|Number of pages||34|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - May 1 2018|
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