Journal of Differential Geometry

Completion of the moduli space for polarized Calabi–Yau manifolds

Yuguang Zhang

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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.

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J. Differential Geom., Volume 103, Number 3 (2016), 521-544.

First available in Project Euclid: 14 July 2016

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Zhang, Yuguang. Completion of the moduli space for polarized Calabi–Yau manifolds. J. Differential Geom. 103 (2016), no. 3, 521--544. doi:10.4310/jdg/1468517503.

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