Speaker
Prof.
Xiaonan Ma
(Institut de Mathématique de Jussieu-Paris Rive Gauche)
Description
We establish an asymptotic version of Bismut's local family index theorem for the Bergman kernel associated with a fiberwise positive line bundle when the power tends to infinity.
The key idea is to use the superconnection as in the local family index theorem. In particular, we show the curvature operator of the associated direct image is a Toeplitz operator.
