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Complete intersections in toric ideals


Authors: Eduardo Cattani, Raymond Curran and Alicia Dickenstein
Journal: Proc. Amer. Math. Soc. 135 (2007), 329-335
MSC (2000): Primary 14M10; Secondary 14M25, 13C40
DOI: https://doi.org/10.1090/S0002-9939-06-08513-3
Published electronically: August 1, 2006
MathSciNet review: 2255278
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Abstract: We present examples that show that in dimension higher than one or codimension higher than two, there exist toric ideals $ I_A$ such that no binomial ideal contained in $ I_A$ and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations.


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Additional Information

Eduardo Cattani
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
Email: cattani@math.umass.edu

Raymond Curran
Affiliation: Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003
Address at time of publication: Department of Mathematical and Computer Sciences, Metropolitan State College of Denver, Denver, Colorado 80202
Email: rcurran@mscd.edu

Alicia Dickenstein
Affiliation: Departamento de Matematica, FCEyN, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Email: alidick@dm.uba.ar

DOI: https://doi.org/10.1090/S0002-9939-06-08513-3
Received by editor(s): January 11, 2005
Received by editor(s) in revised form: August 18, 2005
Published electronically: August 1, 2006
Additional Notes: The first author was partially supported by NSF Grant DMS–0099707
The third author was partially supported by UBACYT X042, Argentina
Communicated by: Michael Stillman
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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