2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62854The main purpose of this notes is to supplement the paper reid, which treated Minimal Model Program (also called Mori's Program) on toric varieties. We calculate lengths of negative extremal rays of toric varieties. As an application, we obtain a generalization of Fujita's conjecture for singular toric varieties. We also prove that every toric variety has a small projective toric $\bQ$-factorialization.11 pages, a new version of RIMS-1340Algebraic Geometry14M25;14E30text