Nagoya Mathematical Journal

Combinatorial descriptions of toric extremal contractions

Hiroshi Sato

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Abstract

In this paper, we give explicit combinatorial descriptions for toric extremal contractions under the relative setting, where varieties are not complete. It is well-known that the complete case is settled by using Reid's wall theory which can not be applied to the non-complete case. Therefore, we can achieve them by using the notion of extremal primitive relations. As applications, we can generalize some of Mustaţă's results related to Fujita's conjecture on toric varieties for the relative case.

Article information

Source
Nagoya Math. J., Volume 180 (2005), 111-120.

Dates
First available in Project Euclid: 14 December 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1134569898

Mathematical Reviews number (MathSciNet)
MR2186671

Zentralblatt MATH identifier
1094.14037

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

Citation

Sato, Hiroshi. Combinatorial descriptions of toric extremal contractions. Nagoya Math. J. 180 (2005), 111--120. https://projecteuclid.org/euclid.nmj/1134569898


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References

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