#### Vol. 301, No. 1, 2019

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BCOV torsion and degenerations of Calabi–Yau manifolds

### Wei Xia

Vol. 301 (2019), No. 1, 351–369
##### Abstract

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.

##### Keywords
BCOV torsion, Calabi–Yau manifolds, degenerations
##### Mathematical Subject Classification 2010
Primary: 14C30, 14D06, 14H15, 14J32, 32G20