Betti numbers of piecewiselex ideals
Commutative Algebra
2021-02-25 v2
Abstract
We extend a result of Caviglia and Sbarra to a polynomial ring with base field of any characteristic. Given a homogeneous ideal containing both a piecewise lex ideal and an ideal generated by powers of the variables, we find a lex ideal with the following property: the ideal in the polynomial ring generated by the piecewise lex ideal, the ideal of powers, and the lex ideal has the same Hilbert function and Betti numbers at least as large as those of the original ideal.
Cite
@article{arxiv.1502.05014,
title = {Betti numbers of piecewiselex ideals},
author = {Christina Jamroz and Gabriel Sosa},
journal= {arXiv preprint arXiv:1502.05014},
year = {2021}
}
Comments
4 pages; replaced a reference, fixed typos, clarified proof of Theorem 10, added Remark 3