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2016 The Buchberger resolution
Anda Olteanu, Volkmar Welker
J. Commut. Algebra 8(4): 571-587 (2016). DOI: 10.1216/JCA-2016-8-4-571

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.

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Anda Olteanu. Volkmar Welker. "The Buchberger resolution." J. Commut. Algebra 8 (4) 571 - 587, 2016. https://doi.org/10.1216/JCA-2016-8-4-571

Information

Published: 2016
First available in Project Euclid: 27 October 2016

zbMATH: 1352.05058
MathSciNet: MR3566531
Digital Object Identifier: 10.1216/JCA-2016-8-4-571

Subjects:
Primary: 05C10, 13C14, 13D02

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.8 • No. 4 • 2016
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