BCOV torsion and degenerations of Calabi–Yau manifolds

Wei Xia

Vol. 301 (2019), No. 1, 351–369

DOI: 10.2140/pjm.2019.301.351

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

Milestones

Received: 10 September 2017

Revised: 27 October 2018

Accepted: 4 December 2018

Published: 16 September 2019