Low-genus primitive monodromy groups with a nonunique minimal normal subgroup

Abstract

Let $X$ be a Riemann surface, and let $f:X\to {\mathbb{P}}_{\mathbb{C}}^1$ be an indecomposable (branched) covering of genus $g$ and degree $n$ whose monodromy group has more than one minimal normal subgroup. Closing a gap in the literature, we show that there is only one such covering when $g\le 1$. Moreover, for arbitrary $g$, there are no such coverings with $n{\gg }_{g}0$ sufficiently large.

12 pages