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.
"Fujita's very ampleness conjecture for singular toric varieties." Tohoku Math. J. (2) 58 (3) 447 - 459, 2006. https://doi.org/10.2748/tmj/1163775140