BCOV TORSION AND DEGENERATIONS OF CALABI-YAU MANIFOLDS

The Fang-Lu formula is an identity relating the Weil-Petersson metric, the generalized Hodge metrics and the BCOV torsion on the moduli space of polarized Calabi-Yau manifolds. In this note, we extend this formula to the compactification of the moduli space of polarized Calabi-Yau manifolds assuming the logarithm of BCOV torsion is locally L-1-integrable. On the other hand, we use this extended formula to study global numerical properties for polarized families of Calabi-Yau manifolds.