2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59411In this short note, we determine the Kodaira dimension and some of the plurigenera of (a desingularization of) a symmetric power of a smooth projective variety. We use it to obtain bounds on the genus of curve passing through a fixed number of general points.4 pages, latexAlgebraic Geometrytext