NOTES ON TORIC VARIETIES FROM MORI THEORETIC VIEWPOINT

Abstract

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's Program) on toric varieties. We compute lengths of negative extremal rays of toric varieties. As an application, a generalization of Fujita's conjecture for singular toric varieties is obtained. We also prove that every toric variety has a small projective toric $\boldsymbol{Q}$-factorialization.