Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution
Commutative Algebra
2013-06-13 v4 Combinatorics
Abstract
In this paper we extend one direction of Fr\"oberg's theorem on a combinatorial classification of quadratic monomial ideals with linear resolutions. We do this by generalizing the notion of a chordal graph to higher dimensions with the introduction of d-chorded and orientably-d-cycle-complete simplicial complexes. We show that a certain class of simplicial complexes, the d-dimensional trees, correspond to ideals having linear resolutions over fields of characteristic 2 and also give a necessary combinatorial condition for a monomial ideal to be componentwise linear over all fields.
Cite
@article{arxiv.1209.5089,
title = {Chorded complexes and a necessary condition for a monomial ideal to have a linear resolution},
author = {Emma Connon and Sara Faridi},
journal= {arXiv preprint arXiv:1209.5089},
year = {2013}
}
Comments
Revised to appear in Journal of Combinatorial Theory, Series A