2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63990We prove the irreducibility of the space parametrizing branched covers of a fixed Riemann surface $B$ of degree $d$, with at least 2d branch points, and with monodromy group equal to $S_d$. The result is classical for $g(B)=0$. The result is well-known for $g(B) > 0$, but we could find no reference.15 pages, 9 figuresAlgebraic GeometryAlgebraic Topology14H30; 57M12text