Tohoku Mathematical Journal

Equivariant completions of toric contraction morphisms

Osamu Fujino

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1163775132

Digital Object Identifier
doi:10.2748/tmj/1163775132

Mathematical Reviews number (MathSciNet)
MR2273272

Zentralblatt MATH identifier
1127.14047

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

Keywords
Toric varieties Mori theory minimal model program equivariant completion

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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