Abstract:

I will explain what dimensional restrictions on the fixed locus of an abelian group
acting on a smooth projective variety come from the Chern numbers of the ambient variety.
The main case of interest is the problem of finding dimensional lower bounds in the case
of p-group actions. This is achieved by constructing explicit examples of actions with
low dimensional fixed locus, and showing that those "exhaust the possibilities" by
analyzing the equivariant cobordism ring.