BCOV invariant and blow-up

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 Kähler 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.

51 pages

References in corpus (1)

• On genus one mirror symmetry in higher dimensions and the BCOV conjectures

Cited by in corpus (1)

• Motivic integration and the birational invariance of BCOV invariants