Abstract:
The Krichever-Hohn elliptic genus of a smooth variety encodes certain (linear combinations of) Chern numbers of the variety. It has been shown to capture exactly the Chern numbers that are invariant under $K$-equivalences. Elliptic genus can also be defined for smooth Deligne-Mumford stacks, as well as for Kawamata log-terminal pairs. One can conjecture that it is invariant under $K$-equivalences of DM stacks. In a joint paper with A.Libgober we have proved this conjecture in the global quotient case, which amounts to the McKay correspondence for elliptic genera. I will give an overview of the problem and the proof and will state open questions related to the notion of elliptic genus.
