Nagoya Mathematical Journal

Combinatorial descriptions of toric extremal contractions

Hiroshi Sato

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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

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

First available in Project Euclid: 14 December 2005

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Mathematical Reviews number (MathSciNet)

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


Sato, Hiroshi. Combinatorial descriptions of toric extremal contractions. Nagoya Math. J. 180 (2005), 111--120.

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