Canonical Hilbert-Burch matrices for power series

Roser Homs Pons and Anna-Lena Winz

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Submission date: 14. Apr. 2020
Pages: 26
Bibtex
MSC-Numbers: 13D02, 14C05
Keywords and phrases: Hilbert-Burch matrices, Gröbner cells, local ordering
Link to arXiv: See the arXiv entry of this preprint.

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.