12/3/2004

Hao Fang
Institute for Advanced Study

Analytic torsion on Calabi-Yau three-folds

We study the analytic torsion on Calabi-Yau manifolds and define a holomorphic invariant modifying the so called BCOV torsion. We study the asymptotic behavior of the new invariant near a singular Calabi-Yau variety;  especially for Calabi-Yau with only ODP singularity. The result is a current curvature formula for Calabi-Yau three-folds. As an application, we verify a conjecture of Beshadsky-Ceccotti-Ooguri-Vafa. In many examples, we link our invariant to automorphic forms. This is a recent joint work with Z. Lu and K.-I. Yoshikawa.