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arXiv · 2003.03805

BCOV invariant and blow-up

Yeping Zhang
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Abstract

Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is called the BCOV invariant. In this paper, we extend the BCOV invariant to such pairs $(X,D)$, where $X$ is a compact K\"ahler manifold and $D$ is a pluricanonical divisor on X with simple normal crossing support. We also study the behavior of the extended BCOV invariant under blow-up. The results in this paper lead to a joint work with Fu proving that birational Calabi-Yau manifolds have the same BCOV invariant.

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Yeping Zhang. 2020-03-08. BCOV invariant and blow-up. https://arxiv.org/abs/2003.03805

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