English

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