English

On the diameter of an ideal

Commutative Algebra 2017-05-10 v1 Combinatorics

Abstract

We begin the study of the notion of diameter of an ideal I of a polynomial ring S over a field, an invariant measuring the distance between the minimal primes of I. We provide large classes of Hirsch ideals, i.e. ideals with diameter not larger than the codimension, such as: quadratic radical ideals of codimension at most 4 and such that S/I is Gorenstein, or ideals admitting a square-free complete intersection initial ideal.

Keywords

Cite

@article{arxiv.1705.03210,
  title  = {On the diameter of an ideal},
  author = {Michela Di Marca and Matteo Varbaro},
  journal= {arXiv preprint arXiv:1705.03210},
  year   = {2017}
}