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Abstract
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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
-integrable.
On the other hand, we use this extended formula to study global numerical
properties for polarized families of Calabi–Yau manifolds.
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Keywords
BCOV torsion, Calabi–Yau manifolds, degenerations
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Mathematical Subject Classification 2010
Primary: 14C30, 14D06, 14H15, 14J32, 32G20
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Milestones
Received: 10 September 2017
Revised: 27 October 2018
Accepted: 4 December 2018
Published: 16 September 2019
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