Resumen de Motivic integration and birational invariance of BCOV invariants

Lie Fu, Yeping Zhang

• Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi–Yau manifolds, which is now called the BCOV torsion. Based on it, a metric-independent invariant, called BCOV invariant, was constructed by Fang–Lu–Yoshikawa and Eriksson–Freixas i Montplet–Mourougane. The BCOV invariant is conjecturally related to the Gromov–Witten theory via mirror symmetry. Based upon previous work of the second author, we prove the conjecture that birational Calabi–Yau manifolds have the same BCOV invariant. We also extend the construction of the BCOV invariant to Calabi–Yau varieties with Kawamata log terminal singularities, and prove its birational invariance for Calabi–Yau varieties with canonical singularities. We provide an interpretation of our construction using the theory of motivic integration.