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

By Anargyros Katsabekis and Ignacio Ojeda

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.Comment: 17 pages; fixed typos, added some clarifying remarks, minor corrections to the original version. Accepted for publication in Pacific Journal of Mathematic

Topics: Mathematics - Commutative Algebra, 13F20 (Primary) 16W50, 13F55 (Secondary)
Year: 2013
DOI identifier: 10.2140/pjm.2014.268.95
OAI identifier: oai:arXiv.org:1103.4702
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