Journal of Commutative Algebra

The Buchberger resolution

Anda Olteanu and Volkmar Welker

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

First available in Project Euclid: 27 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Monomial resolution cellular resolution Scarf complex minimal free resolution


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

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