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Generalized Hodge Metrics and BCOV torsion on Calabi-Yau Moduli

Hao Fang·Zhiqin Lu
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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 Poincaré metric.

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Hao Fang, Zhiqin Lu. 2003-10-01. Generalized Hodge Metrics and BCOV torsion on Calabi-Yau Moduli. https://arxiv.org/abs/math/0310007

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