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CRITICAL BINOMIAL IDEALS OF NORTHCOTT TYPE
Published online by Cambridge University Press: 16 November 2020
Abstract
In this paper, we study a family of binomial ideals defining monomial curves in the n-dimensional affine space determined by n hypersurfaces of the form $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}}$ in $\Bbbk [x_1, \ldots , x_n]$ with $u_{ii} = 0, \ i\in \{ 1, \ldots , n\}$ . We prove that the monomial curves in that family are set-theoretic complete intersections. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Frobenius number of the corresponding numerical semigroup. We also describe a method to produce set-theoretic complete intersection semigroup ideals of arbitrary large height.
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- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
Communicated by James East
The authors were supported by the project MTM2017-84890-P, which is funded by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER. The first and third authors were also partially supported by the project PGC2018-096446-B-C21 (MINECO/FEDER, UE). The first and second authors were supported by the Junta de Andalucía Grant Number FQM-343, and the third author was supported by the Junta de Extremadura Grant Number FQM024-GR18021 (FEDER, UE).