Admissible cover cycles in the moduli space of stable curves

Inside the moduli space of stable curves there are closed
subsets defined by the condition that the curve C admits a finite cover
of a second curve D with specified ramification behavior. I will show
how these sets can be parametrized by nice smooth and proper moduli
spaces. In many cases, this parametrization can be used to compute the
fundamental class of such admissible cover loci in the cohomology group
of the moduli space. This is joint work with Jason van Zelm.