A local index theorem for complex manifolds with C* action
A local index theorem for complex manifolds with C* action

JihHsin Cheng, Institute of Mathematics, Academia Sinica
Fine Hall 314
Suppose N is a complex manifold with a holomorphic C* action $\sigma (re^{ia})$. Assume $\sigma (r)$ is globally free, $\sigma (e^{ia})$ is locally free and the orbit space M=N/$\sigma$ is compact. Then we have a local index theorem for N through a heat kernel approach. As an application, the singular strata in Kawasaki's RiemannRoch theorem for the compact complex orbifold M have no contribution.
This is joint work with ChinYu Hsiao and IHsun Tsai.