On a compactification of a Hurwitz space in the wild case

Abstract

Let $g$ and $g^{\prime }$ be two integers and $p$ a prime number. Denote by ${\mathcal{H}}_{g,g^{\prime },p}^c$ the moduli space of morphisms of degree $p$ between smooth curves of genus $g$ and $g^{\prime }$ and with constant ramification. The purpose of this article is to construct and describe a modular compactification of this space.

30 pages