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arXiv · 1103.4702

An indispensable classification of monomial curves in $\mathbb{A}^4(\mathbbmss{k}) $

Anargyros Katsabekis·Ignacio Ojeda
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Abstract

In this paper a new classification of monomial curves in $\mathbb{A}^4(\mathbbmss{k})$ is given. Our classification relies on the detection of those binomials and monomials that have to appear in every system of binomial generators of the defining ideal of the monomial curve; these special binomials and monomials are called indispensable in the literature. This way to proceed has the advantage of producing a natural necessary and sufficient condition for the definining ideal of a monomial curve in $\mathbb{A}^4(\mathbbmss{k})$ to have a unique minimal system of binomial generators. Furthermore, some other interesting results on more general classes of binomial ideals with unique minimal system of binomial generators are obtained.

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Anargyros Katsabekis, Ignacio Ojeda. 2011-03-24. An indispensable classification of monomial curves in $\mathbb{A}^4(\mathbbmss{k}) $. https://doi.org/10.2140/pjm.2014.268.95

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