Tohoku Mathematical Journal

Equivariant completions of toric contraction morphisms

Osamu Fujino

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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

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

First available in Project Euclid: 17 November 2006

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Zentralblatt MATH identifier

Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)

Toric varieties Mori theory minimal model program equivariant completion


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

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