2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63904We study subvarieties of a general projective degree $d$ hypersurface $X_d\subset \mathbf P^n$. Our main theorem, which improves previous results of L. Ein and C. Voisin, implies in particular the following sharp corollary: any subvariety of a general hypersurface $X_{d}\subset {\mathbf P}^n$, for $n\geq 6$ and $d\geq 2n-2$, is of general type.Title changed, introduction completely rewritten, exposition improved. To appear in the Transactions of the A.M.S. 18 pages, LatexAlgebraic Geometry14J70; 14K12; 14C99; 32Q45text