2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72250In this paper, we give an affirmative answer to a conjecture in the Minimal Model Program. We prove that log $Q$-Fano varieties of dim $n$ are rationally connected. We also study the behavior of the canonical bundles under projective morphisms.Minor modifications. To appear in J. reine angew. MathAlgebraic Geometrytext