Abstract: The BCOV invariant, named after Bershadsky, Cecotti, Ooguri and Vafa, is a real-valued invariant of Calabi-Yau manifolds constructed from Ray-Singer's analytic torsion. They are conjectured to encode the genus-1 Gromov-Witten invariant under mirror symmetry. Based on the previous study of Yeping Zhang, we show that birationally equivalent Calabi-Yau manifolds have the same BCOV invariant, confirming a conjecture of Fang-Lu-Yoshikawa and Eriksson-Freixas i Montplet-Mourougane. One key construction in our proof comes from the theory of motivic integration. This is a joint work with Yeping Zhang.
https://wwu.zoom.us/j/98750589020