2014/08/30 by Kenichi Yoshikawa, Ken-Ichi Yoshikawa, Yoshikawa, Ken-Ichi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #math.AG #math.DG
paper · pdf · doi:10.48550/arxiv.1409.0127
arxiv created 2014/08/30 · openalex publication_date 2014/08/30 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In their papers published in 1993 and 1994, by expressing certain physical quantity in two distinct ways, Bershadsky-Cecotti-Ooguri-Vafa discovered a remarkable equivalence between Ray-Singer analytic torsion and elliptic instanton numbers for Calabi-Yau threefolds. After their discovery, in a paper published in 2008, a holomorphic torsion invariant for Calabi-Yau threefolds corresponding to the physical quantity was constructed and is called BCOV invariant. In this article, we study the asymptotic behavior of BCOV invariants for algebraic one-parameter degenerations of Calabi-Yau threefolds. We prove the rationality of the coefficient of logarithmic divergence and give its geometric expression by using a semi-stable reduction of the given family.