2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71156We prove the $\mathbb{Q}$-factoriality of a nodal hypersurface in $\mathbb{P}^{4}$ of degree $n$ with at most ${\frac{(n-1)^{2}}{4}}$ nodes and the $\mathbb{Q}$-factoriality of a double cover of $\mathbb{P}^{3}$ branched over a nodal surface of degree $2r$ with at most ${\frac{(2r-1)r}{3}}$ nodes.28 pages, in the last version we change the introductionAlgebraic Geometry14J30, 14J17, 14J70, 14E07, 14E08, 14J45text