We 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.Comment: 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.
