Generators for the derivation modules and the relation ideals of certain curves (Q752118)

Let \({\mathcal O}\) be a reduced and irreducible curve in the affine algebroid e-space over a field K of characteristic zero. Let \({\mathcal D}=Der_ K({\mathcal O})\) and let P be the relation ideal of \({\mathcal O}\). This paper is closely related to the authors' preprint ``Generators for the derivation modules and the prime ideals of certain curves''. The goal is to find bounds for the minimal number of generators (usually by producing a generating set) for \({\mathcal D}\) and for P, at least for certain kinds of curves. In the paper under review the authors consider the case where \({\mathcal O}\) is a monomial curve defined by an almost arithmetic sequence (i.e. a sequence of e terms where some e-1 of them form an arithmetic sequence). Here \(\mu\) (\({\mathcal D})\leq 2e-3\) and \(\mu\) (P)\(\leq e(e-1)/2\), and in fact the authors produce generating sets in both cases. The main tool is an explicit description of a standard basis of the semigroup generated by an almost exact sequence.