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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.

MiS Preprint
46/2020

Canonical Hilbert-Burch matrices for power series

Roser Homs Pons and Anna-Lena Winz

Abstract

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.

Received:
Apr 14, 2020
Published:
Apr 17, 2020
MSC Codes:
13D02, 14C05
Keywords:
Hilbert-Burch matrices, Gröbner cells, local ordering

Related publications

inJournal
2021 Repository Open Access
Roser Homs and Anna-Lena Winz

Canonical Hilbert-Burch matrices for power series

In: Journal of algebra, 583 (2021), pp. 1-24