Compactifying spaces of branched covers
Compactifying spaces of branched covers

Anand Deopurkar , Columbia University
Fine Hall 322
Moduli spaces of geometrically interesting objects are often noncompact. They need to be compactified by adding some degenerate objects. In many cases, this can be done in several ways, leading to a menagerie of birational models, which are related to each other in interesting ways. In this talk, I will explore this idea for the spaces of branched covers of curves, known as the Hurwitz spaces. I will construct a number of compactifications of these spaces by allowing more and more branch points to coincide. I will describe the geometry of the resulting spaces for the case of triple covers.