2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58600We prove finiteness of the number of smooth blow-downs on Fano manifolds and boundedness results for the geometry of non projective Fano-like manifolds. Our proofs use properness of Hilbert schemes and Mori theory.8 pages, also available as a "Prépublication de l'Institut Fourier", http://www-fourier.ujf-grenoble.fr/prepublications.htmlAlgebraic Geometry14J45, 14E30, 14E05, 32J18text