Generalized Hodge metrics and BCOV torsion on Calabi-Yau moduli

  title={Generalized Hodge metrics and BCOV torsion on Calabi-Yau moduli},
  • Published 2006
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… CONTINUE READING

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