2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132222We present a self-contained combinatorial approach to Fujita's conjectures in the toric case. Our main new result is a generalization of Fujita's very ampleness conjecture for toric varieties with arbitrary singularities. In an appendix, we use similar methods to give a new proof of an analogous toric generalization of Fujita's freeness conjecture due to Fujino.15 pages. v2: minor revisions, updated references, added appendix with proof of Fujino's Theorem. v3: minor changes, final version, to appear in Tohoku Math. JAlgebraic GeometryCombinatorics14M25 (Primary) 14C20, 52B20 (Secondary)text