Heat kernel asymptotics and local index theorem for open complex manifolds with C*action
Heat kernel asymptotics and local index theorem for open complex manifolds with C*action

JihHsin Cheng, Academia Sinica
Fine Hall 314
For a complex manifold Σ with C∗action, we define the mth C∗ FourierDolbeault cohomology group and consider the mindex on Σ. By applying the method of transversal heat kernel asymptotics, we obtain a local index formula for the mindex. We can reinterpret Kawasaki’s HirzebruchRiemannRoch formula for a compact complex orbifold with an orbifold holomorphic line bundle by our integral formulas over a (smooth) complex manifold and finitely many complex submanifolds arising from singular strata. This is joint work with ChinYu Hsiao and IHsun Tsai.