Generalized Hodge Metrics and BCOV torsion on Calabi-Yau Moduli
Differential Geometry
2007-05-23 v1 Algebraic Geometry
Abstract
We establish an unexpected relation among the Weil-Petersson metric, the generalized Hodge metrics and the BCOV torsion. Using this relation, we prove that certain kind of moduli spaces of polarized Calabi-Yau manifolds do not admit complete subvarieties. That is, there is no complete family for certain class of polarized Calabi-Yau manifolds. We also give an estimate of the complex Hessian of the BCOV torsion using the relation. After establishing a degenerate version of the Schwarz Lemma of Yau, we prove that the complex Hessian of the BCOV torsion is bounded by the Poincar\'e metric.
Keywords
Cite
@article{arxiv.math/0310007,
title = {Generalized Hodge Metrics and BCOV torsion on Calabi-Yau Moduli},
author = {Hao Fang and Zhiqin Lu},
journal= {arXiv preprint arXiv:math/0310007},
year = {2007}
}
Comments
Latex file; 20 pages, 0 figure