2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61605We classify complex projective manifolds $X$ for which there exists a point $a$ such that the blow-up of $X$ at $a$ is Fano.7 pages, no figure, in french. Some mistakes communicated to us by an anonymous referee are correctedAlgebraic Geometry14J45;14E30text