A finite classification of \((x, y)\)-primary ideals of low multiplicity
If \(p=(x,y)\) is an ideal generated by two independent linear forms in a polynomial ring \(S\) over an algebraically closed field \(k\), one gives a (finite, i.e. one gives low degree generators) classification of \(p\)-primary ideals of multiplicity \(e(S/I)=3\) or \(e(S/I)=4\). In other contexts, similar classifications for the local case (i.e. rings of formal powers) or multiple structures on lines (or linear spaces) can be found in the papers quoted in the references or in the references of the quoted papers. In the case considered here the lists are particularly long. The authors give a good motivation for the interest of the subject.
scientific article; zbMATH DE number 6841311
scientific article