Amy Li
University of Texas
Title
Intersection theory on the Hurwitz space of admissible covers
Abstract
The Hurwitz space is a moduli space parametrizing branched covers of curves. Harris and Mumford introduced the "admissible covers" compactification of the Hurwitz space, in which the target and source curves of a cover degenerate into nodal curves when branch points come together. The boundary of the Hurwitz space is then stratified by lower-dimensional Hurwitz spaces. This structure is strikingly similar to the stratification of the Deligne-Mumford compactification of the moduli space of curves. Inspired by the well-studied intersection theory of the moduli space of curves, we develop new techniques for computing the low degree Chow and cohomology groups of the Hurwitz space. Some of this work is joint with E. Clader, Z. Hu, H. Larson, and R. Lopez.
