2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/214427Here we show that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF in short). Furthermore, if b_{2}^{+}(X)> 0 then it also has a Broken Lefschetz Pencil structure (BLP) with nonempty base locus. This imroves a Theorem of Auroux, Donaldson and Katzarkov, and our proof is topological (i.e. uses 4-dimensional handlebody theory).24 pages, 14 figures, published versionGeometric TopologyAlgebraic Geometry57R55, 57R65, 57R17, 57M50text