English

Monomial ideals with tiny squares

Commutative Algebra 2021-08-17 v1 Combinatorics

Abstract

Let IK[x,y]I \subset K[x,y] be a monomial ideal. How small can μ(I2)\mu(I^2) be in terms of μ(I)\mu(I)? It has been expected that the inequality μ(I2)>μ(I)\mu(I^2) > \mu(I) should hold whenever μ(I)2\mu(I) \ge 2. Here we disprove this expectation and provide a somewhat surprising answer to the above question.

Cite

@article{arxiv.1801.07672,
  title  = {Monomial ideals with tiny squares},
  author = {Shalom Eliahou and Jürgen Herzog and Maryam Mohammadi Saem},
  journal= {arXiv preprint arXiv:1801.07672},
  year   = {2021}
}
R2 v1 2026-06-22T23:53:23.339Z