## Tohoku Mathematical Journal

### Equivariant completions of toric contraction morphisms

Osamu Fujino

#### 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 58, Number 3 (2006), 303-321.

Dates
First available in Project Euclid: 17 November 2006

https://projecteuclid.org/euclid.tmj/1163775132

Digital Object Identifier
doi:10.2748/tmj/1163775132

Mathematical Reviews number (MathSciNet)
MR2273272

Zentralblatt MATH identifier
1127.14047

#### Citation

Fujino, Osamu. Equivariant completions of toric contraction morphisms. Tohoku Math. J. (2) 58 (2006), no. 3, 303--321. doi:10.2748/tmj/1163775132. https://projecteuclid.org/euclid.tmj/1163775132

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