We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the sense of Kollár. This completes Kollár's projectivity criterion for the moduli spaces of higher-dimensional stable varieties.
"Semipositivity theorems for moduli problems." Ann. of Math. (2) 187 (3) 639 - 665, May 2018. https://doi.org/10.4007/annals.2018.187.3.1