2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99088In this paper we study the behaviour of the Lefschetz property under the blow-up construction. We show that it is possible to reduce the dimension of the kernel of the Lefschetz map if we blow up along a suitable submanifold satisfying the Lefschetz property. We use that, together with results about Massey products, to construct nonformal (simply connected) symplectic manifolds satisfying the Lefschetz property.19 pages. Minor changes in the text, typos corrected. To appear in Trans. Amer. Math. SocSymplectic GeometryDifferential Geometry53D35 (primary); 57R19 (Secondary)text