Depth and Singular Varieties of Exterior Edge Ideals
Commutative Algebra
2022-08-09 v1 Combinatorics
Rings and Algebras
Abstract
Edge ideals of finite simple graphs are well-studied over polynomial rings. In this paper, we initiate the study of edge ideals over exterior algebras, specifically focusing on the depth and singular varieties of such ideals. We prove an upper bound on the depth of the edge ideal associated to a general graph and a more refined bound for bipartite graphs, and we show that both are tight. We also compute the depth of several large families of graphs including cycles, complete multipartite graphs, spider graphs, and Ferrers graphs. Finally, we focus on the effect whiskering a graph has on the depth of the associated edge ideal.
Cite
@article{arxiv.2208.03366,
title = {Depth and Singular Varieties of Exterior Edge Ideals},
author = {Matthew Mastroeni and Jason McCullough and Andrew Osborne and Joshua Rice and Cole Willis},
journal= {arXiv preprint arXiv:2208.03366},
year = {2022}
}
Comments
22 pages. Comments welcome