Generalized Hodge metrics and BCOV torsion on Calabi-Yau moduli

Hao Fang, Zhiqin Lu
2005 Journal für die Reine und Angewandte Mathematik  
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 smooth 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
more » ... a of Yau, we prove that the complex Hessian of the BCOV torsion is bounded by the Poincaré metric.
doi:10.1515/crll.2005.2005.588.49 fatcat:yudbngot7ffldasyc3wnprrasi