The core of monomial ideals
Commutative Algebra
2023-03-21 v1
Abstract
The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal satisfying certain residual conditions, showing that coincides with the largest monomial ideal contained in a general reduction of . We prove that the class of lex-segment ideals satisfies these residual conditions and study the core of lex-segment ideals generated in one degree. For monomial ideals that do not necessarily satisfy the residual conditions and that are generated in one degree, we conjecture an explicit formula for the core, and make progress towards this conjecture.
Cite
@article{arxiv.2303.10486,
title = {The core of monomial ideals},
author = {Louiza Fouli and Jonathan Montaño and Claudia Polini and Bernd Ulrich},
journal= {arXiv preprint arXiv:2303.10486},
year = {2023}
}