Notes on toric varieties from Mori theoretic viewpoint

The main purpose of this notes is to supplement the paper by Reid: Decomposition of toric morphisms, which treated Minimal Model Program (also called Mori\u27s Program) on toric varieties. We compute lengths of negative extremal rays of toric varieties. As an application, a generalization of Fujita\u27s conjecture for singular toric varieties is obtained. We also prove that every toric variety has a small projective toric $Q$-factorialization