On a compactification of a Hurwitz space in the wild case

Abstract

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