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arXiv · 1705.10268

Critical binomial ideals of Norhtcott type

P. A. García-Sánchez·D. Llena·I. Ojeda
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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 $x_i^{c_i} - x_1^{u_{i1}} \cdots x_n^{u_{1n}} \in k[x_1, \ldots, x_n]$ with $u_{ii} = 0$, $i\in \{ 1, \ldots, n\}$. We prove that, the monomial curves in that family are set-theoretic complete intersection. Moreover, if the monomial curve is irreducible, we compute some invariants such as genus, type and Fröbenius 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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P. A. García-Sánchez, D. Llena, I. Ojeda. 2017-05-29. Critical binomial ideals of Norhtcott type. https://arxiv.org/abs/1705.10268

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