Analytic torsion for Borcea-Voisin threefolds
Abstract
In their study of genus-one string amplitude, Bershadsky-Cecotti-Ooguri-Vafa discovered a remarkable identification between holomorphic Ray-Singer torsion and instanton numbers for Calabi-Yau threefolds. The holomorphic torsion invariant for Calabi-Yau threefolds corresponding to the genus-one string amplitude is called BCOV invariant. In this paper, we establish an identification between the BCOV invariants of Borcea-Voisin threefolds and another holomorphic torsion invariants for K3 surfaces with involution. We also introduce BCOV invariants for abelian Calabi-Yau orbifolds. Between Borcea-Voisin orbifold and its crepant resolution, we compare their BCOV invariants.
Keywords
Cite
@article{arxiv.1410.0212,
title = {Analytic torsion for Borcea-Voisin threefolds},
author = {Ken-Ichi Yoshikawa},
journal= {arXiv preprint arXiv:1410.0212},
year = {2016}
}
Comments
definition of BCOV invariants extended to general abelian CY orbifolds; curvature formula given