Journal of Commutative Algebra

The Buchberger resolution

Anda Olteanu and Volkmar Welker

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Abstract

We define the Buchberger resolution, which is a graded free resolution of a monomial ideal in a polynomial ring. Its construction uses a generalization of the Buchberger graph and encodes much of the combinatorics of the Buchberger algorithm. The Buchberger resolution is a cellular resolution that, when it is minimal, coincides with the Scarf resolution. The simplicial complex underlying the Buchberger resolution is of interest for its own sake, and its combinatorics is not fully understood. We close with a conjecture on the clique complex of the Buchberger graph.

Article information

Source
J. Commut. Algebra, Volume 8, Number 4 (2016), 571-587.

Dates
First available in Project Euclid: 27 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.jca/1477600748

Digital Object Identifier
doi:10.1216/JCA-2016-8-4-571

Mathematical Reviews number (MathSciNet)
MR3566531

Zentralblatt MATH identifier
1352.05058

Subjects
Primary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25] 13C14: Cohen-Macaulay modules [See also 13H10] 13D02: Syzygies, resolutions, complexes

Keywords
Monomial resolution cellular resolution Scarf complex minimal free resolution

Citation

Olteanu, Anda; Welker, Volkmar. The Buchberger resolution. J. Commut. Algebra 8 (2016), no. 4, 571--587. doi:10.1216/JCA-2016-8-4-571. https://projecteuclid.org/euclid.jca/1477600748


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