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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Set-theoretic complete intersections on binomials


Authors: Margherita Barile, Marcel Morales and Apostolos Thoma
Journal: Proc. Amer. Math. Soc. 130 (2002), 1893-1903
MSC (2000): Primary 14M25, 13C40, 14M10
Published electronically: December 20, 2001
MathSciNet review: 1896020
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Abstract: Let $V$ be an affine toric variety of codimension $r$over a field of any characteristic. We completely characterize the affine toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that in the characteristic zero case, $V$is a set-theoretic complete intersection on binomials if and only if $V$ is a complete intersection. Moreover, if $F_1,\dots ,F_r$ are binomials such that $I(V) = rad(F_1,\dots, F_r)$, then $I(V) = (F_1,\dots,F_r)$. While in the positive characteristic $p$ case, $V$ is a set-theoretic complete intersection on binomials if and only if $V$ is completely $p$-glued.

These results improve and complete all known results on these topics.


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Additional Information

Margherita Barile
Affiliation: Dipartimento di Matematica, Università degli Studi di Bari, Via Orabona 4, 70125 Bari, Italy
Email: barile@dm.uniba.it

Marcel Morales
Affiliation: Université de Grenoble I, Institut Fourier, UMR 5582, B.P.74, 38402 Saint-Martin D’Hères Cedex, and IUFM de Lyon, 5 rue Anselme, 69317 Lyon Cedex, France
Email: Marcel.Morales@ujf-grenoble.fr

Apostolos Thoma
Affiliation: Department of Mathematics, Purdue Univerity, West Lafayette, Indiana 47907-1395
Address at time of publication: Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
Email: athoma@cc.uoi.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06289-X
PII: S 0002-9939(01)06289-X
Keywords: Affine semigroups, binomial ideals, complete intersections, set-theoretic complete intersections, toric varieties
Received by editor(s): October 17, 2000
Received by editor(s) in revised form: January 16, 2001
Published electronically: December 20, 2001
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2001 American Mathematical Society