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arXiv · 1409.0127

Degenerations of Calabi-Yau threefolds and BCOV invariants

Ken-Ichi Yoshikawa
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Abstract

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.

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Ken-Ichi Yoshikawa. 2014-08-30. Degenerations of Calabi-Yau threefolds and BCOV invariants. https://arxiv.org/abs/1409.0127

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