In this paper, we construct a completion of the moduli space for polarized Calabi–Yau manifolds by using Ricci-flat Kähler–Einstein metrics and the Gromov–Hausdorff topology, which parameterizes certain Calabi–Yau varieties. We then study the algebro-geometric properties and the Weil–Petersson geometry of such completion. We show that the completion can be exhausted by sequences of quasi-projective varieties, and new points added have finite Weil–Petersson distance to the interior.
"Completion of the moduli space for polarized Calabi–Yau manifolds." J. Differential Geom. 103 (3) 521 - 544, July 2016. https://doi.org/10.4310/jdg/1468517503