Vol. 301, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 301: 1
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Vol. 297: 1  2
Vol. 296: 1  2
Vol. 295: 1  2
Vol. 294: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
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 L1-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
Authors
Wei Xia
School of Mathematics
Sun Yat-sen University
Guangzhou
China