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Combinatorial descriptions of toric extremal Contractions

Published online by Cambridge University Press:  11 January 2016

Hiroshi Sato
Hiroshi Sato*
Affiliation:
Department of Mathematics Tokyo Institute of Technology 2-12-1 Oh-Okayama Meguro-ku Tokyo, 152-8551Japanhirosato@math.titech.ac.jp
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Abstract

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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.

Keywords

14M2514E30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 180 , 2005 , pp. 112 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

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