2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150148We prove that for any smooth projective variety $X$ of dimension $\geq 3$, there exists an integer $g_0=g_0(X)$, such that for any integer $g \geq g_0$, there exists a smooth curve $C$ in $X$ with $g(C)=g$.AMS-Tex, 5 pagesAlgebraic GeometryOn Genera of Smooth Curves in Higher Dimensional Varietiestext