Compactifications of hurwitz spaces

Abstract

We construct several modular compactifications of the Hurwitz space of genus g curves expressed as d-sheeted, simply branched covers of genus h curves. These compactifications are obtained by allowing the branch points of the covers to collide to a variable extent. They are well behaved if d=2,3, or if relatively few collisions are allowed. We recover as special cases the spaces of twisted admissible covers of Abramovich, Corti, and Vistoli and the spaces of hyperelliptic curves of Fedorchuk. Show more