Journal of Commutative Algebra

Acyclic digraphs giving rise to complete intersections

Walter D. Morris, Jr

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Abstract

We call a directed acyclic graph a CI-digraph if a certain affine semigroup ring defined by it is a complete intersection. We show that if $D$ is a 2-connected CI-digraph with cycle space of dimension at least 2, then it can be decomposed into two subdigraphs, one of which can be taken to have only one cycle, that are CI-digraphs and are glued together on a directed path. If the arcs of the digraph are the covering relations of a poset, this is the converse of a theorem of Boussicault, Feray, Lascoux and Reiner. The decomposition result shows that CI-digraphs can be easily recognized.

Article information

Source
J. Commut. Algebra, Volume 11, Number 2 (2019), 241-264.

Dates
First available in Project Euclid: 24 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.jca/1561363360

Digital Object Identifier
doi:10.1216/JCA-2019-11-2-241

Mathematical Reviews number (MathSciNet)
MR3973139

Subjects
Primary: 14M10: Complete intersections [See also 13C40]
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65] 05C20: Directed graphs (digraphs), tournaments

Keywords
Complete intersection cycle basis directed graph

Citation

Jr, Walter D. Morris,. Acyclic digraphs giving rise to complete intersections. J. Commut. Algebra 11 (2019), no. 2, 241--264. doi:10.1216/JCA-2019-11-2-241. https://projecteuclid.org/euclid.jca/1561363360


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