2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136756An Artinian ideal $I$ of $k[x,y]$ has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Gröbner cells and their Betti strata recovering results of Ellingsrud and Strømme, Göttsche and Iarrobino.Commutative AlgebraAlgebraic Geometry13P10, 14C05text