Completion of the moduli space for polarized Calabi-Yau manifolds
Differential Geometry
2015-02-10 v3 Algebraic Geometry
Metric Geometry
Abstract
In this paper, we construct a completion of the moduli space for polarized Calabi-Yau manifolds by using Ricci-flat K\"ahler-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.
Keywords
Cite
@article{arxiv.1410.2979,
title = {Completion of the moduli space for polarized Calabi-Yau manifolds},
author = {Yuguang Zhang},
journal= {arXiv preprint arXiv:1410.2979},
year = {2015}
}
Comments
Comments are welcomed. Revised argument, results unchanged