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arXiv · 1410.2979

Completion of the moduli space for polarized Calabi-Yau manifolds

Yuguang Zhang
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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.

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Yuguang Zhang. 2015-02-08. Completion of the moduli space for polarized Calabi-Yau manifolds. https://arxiv.org/abs/1410.2979

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