# BCOV invariant and birational equivalence

2019/05/24 Fri 10:30 - 12:00

3号館152号室

Yeping Zhang

Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair $(X,Y)$, where $X$ is a Kaehler manifold and $Y\subseteq X$ is a pluricanonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.