The Principal Component of the Jets of a Graph
Commutative Algebra
2022-01-13 v1 Algebraic Geometry
Combinatorics
Abstract
We define the s-order principal component of the jets of a graph and give a description of the primary decomposition of its edge ideal in terms of the minimal vertex covers of the base graph. As an application, we show the s-order principal component of the jets of a cochordal graph is cochordal, and connect this to Froberg's theorem on the linear resolution of edge ideals of cochordal graphs. An appendix is provided describing some computations of jets in the computer algebra system Macaulay2.
Keywords
Cite
@article{arxiv.2201.04164,
title = {The Principal Component of the Jets of a Graph},
author = {Nicholas Iammarino},
journal= {arXiv preprint arXiv:2201.04164},
year = {2022}
}