2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122138We prove that the moduli space ${\Cal M}_{g,n}$ of smooth curves of genus $g$ with $n$ marked points is rational for $g=6$ and $1 \le n \le 8$, and it is unirational for $g=8$ and $1 \le n \le 11$, $g=10$ and $1 \le n \le 3$, $g=12$ and $n = 1$.Algebraic Geometry14H10, 14H45, 14E08, 14L30text