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Proceedings of the American Mathematical Society

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On systems of binomials in the ideal of a toric variety

Authors: Shalom Eliahou and Rafael H. Villarreal
Journal: Proc. Amer. Math. Soc. 130 (2002), 345-351
MSC (2000): Primary 13F20; Secondary 14H45
Published electronically: June 6, 2001
MathSciNet review: 1862111
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Abstract: Let $\Gamma$ be a toric set in the affine space ${\mathbb A}_k^n$. Given a set of binomials $g_1,\ldots,g_r$ in the toric ideal $P$ of $\Gamma$, we give a criterion for deciding the equality rad( $g_1,\ldots,g_r$) = $P$. This criterion extends to arbitrary dimension, and to arbitrary fields, an earlier result which concerned only monomial curves over an algebraically closed field of characteristic zero.

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Additional Information

Shalom Eliahou
Affiliation: Université du Littoral, LMPA Joseph Liouville, Bâtiment H. Poincaré-50 rue F. Buisson, BP 699 - 62228 Calais Cédex, France

Rafael H. Villarreal
Affiliation: Departamento de Matemáticas, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14–740, 07000 México City, D.F., Mexico

Keywords: Toric variety, monomial curve, binomial ideal
Received by editor(s): February 14, 2000
Received by editor(s) in revised form: June 22, 2000
Published electronically: June 6, 2001
Additional Notes: This work was partially supported by CONACyT grant 27931E and SNI, México
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society