2020/03/08 by Yeping Zhang, Zhang, Yeping
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.2003.03805
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.