Tohoku Mathematical Journal
2006
September
SECOND SERIES VOL. 58, NO. 3

Tohoku Math. J.
58 (2006), 303-321

Title EQUIVARIANT COMPLETIONS OF TORIC CONTRACTION MORPHISMS

Author Osamu Fujino

(Received July 14, 2004, revised May 11, 2005)
Abstract. We treat equivariant completions of toric contraction morphisms as an application of the toric Mori theory. For this purpose, we generalize the toric Mori theory for non-$\boldsymbol Q$-factorial toric varieties. So, our theory seems to be quite different from Reid's original combinatorial toric Mori theory. We also explain various examples of non-$\boldsymbol Q$-factorial contractions, which imply that the $\boldsymbol Q$-factoriality plays an important role in the Minimal Model Program. Thus, this paper completes the foundation of the toric Mori theory and shows us a new aspect of the Minimal Model Program.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14E30.
Key words and phrases. Toric varieties, Mori theory, minimal model program, equivariant completion.

To the top of this page

Back to the Contents