Bounded regularity
If \(S\) is a polynomial ring and \(M\) a finitely generated graded \(S\)-module, the author introduces the notion of a sequence \((f_1,\dots,f_r)\) of homogeneous polynomials which is regular up to a certain degree. For general modules \(M\), he then provides two characterisations of sequences regular up to a degree \(D\): one in terms of the Hilbert series of \(M/(f_1,\dots,f_r)M\) and one in terms of first syzygies. For the special case \(M=S\), two further characterisations are given: one via Betti numbers and one via the Koszul complex of the sequence and the minimal free resolution of the ideal generated by the sequence. Some applications of the results, in particular to the analysis of Faugeère's F5 algorithm for Gröbner bases computations, are given.
scientific article; zbMATH DE number 6377609
scientific article