Completion of the moduli space for polarized Calabi-Yau manifolds

Abstract

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 perperties 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.

Comments are welcomed. Revised argument, results unchanged

References in corpus (2)

• Singular Kahler-Einstein metrics
• Families of Calabi-Yau manifolds and canonical singularities