An indispensable classification of monomial curves in $\mathbb{A}^4(\mathbbmss{k}) $
arXiv:1103.4702 · doi:10.2140/pjm.2014.268.95
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.
17 pages; fixed typos, added some clarifying remarks, minor corrections to the original version. Accepted for publication in Pacific Journal of Mathematics