We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
We give a parametrization of zero-dimensional ideals in the power series ring $k[[x,y]]$ with a given leading term ideal with respect to local lex ordering in terms of certain canonical Hilbert-Burch matrices. This is an extension to the local setting of the parametrizations of Gröbner cells obtained in the polynomial ring $k[x,y]$ by Conca and Valla for lex ordering and Constantinescu for deglex.
