Tohoku Mathematical Journal
2003
December
SECOND SERIES VOL. 55, NO. 4

Tohoku Math. J.
55 (2003), 551-564

Title NOTES ON TORIC VARIETIES FROM MORI THEORETIC VIEWPOINT

Author Osamu Fujino

(Received December 13, 2001, revised August 26, 2002)
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 $Q$-factorialization.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14E30.

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