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

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Jih-Hsin 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 Riemann-Roch theorem for the compact complex orbifold M have no contribution.

This is joint work with Chin-Yu Hsiao and I-Hsun Tsai.