Complete intersections in toric ideals
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- by Eduardo Cattani, Raymond Curran and Alicia Dickenstein PDF
- Proc. Amer. Math. Soc. 135 (2007), 329-335 Request permission
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.References
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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
- MR Author ID: 57755
- Email: alidick@dm.uba.ar
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2255278