Relation between regularity of powers of edge ideals and (im, reg)-invariant extension

Hiroju Kanno

Relation between regularity of powers of edge ideals and (im, reg)-invariant extension

Commutative Algebra 2020-07-14 v2 Combinatorics

Authors: Hiroju Kanno

Abstract

In this paper, we define (im, reg)-invariant extension of graphs and propose a new approach for Nevo and Peeva's conjecture which said that for any gap-free graph $G$ with $reg(I(G)) = 3$ and for any $k \geq 2$ , $I(G)^k$ has a linear resolution. Moreover, we consider new conjectures related to the regularity of powers of edge ideals of gap-free graphs.

Keywords

edge ideals regularity powers of ideals gap-free graphs linear resolution (im, reg)-invariant extension monomial ideals

Cite

@article{arxiv.2003.05419,
  title  = {Relation between regularity of powers of edge ideals and (im, reg)-invariant extension},
  author = {Hiroju Kanno},
  journal= {arXiv preprint arXiv:2003.05419},
  year   = {2020}
}

Comments

7 pages

Related papers

View all related →