Analytic torsion for Borcea-Voisin threefolds

2014/10/01 by Kenichi Yoshikawa, Ken-Ichi Yoshikawa, Yoshikawa, Ken-Ichi
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1410.0212

definition of BCOV invariants extended to general abelian CY orbifolds; curvature formula given

openalex publication_date 2014/10/01 · arxiv created 2016/02/09 · arxiv updated 2016/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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