Hilbert depth of graded modules over polynomial rings in two variables
Commutative Algebra
2012-08-02 v2 Combinatorics
Abstract
In this article we mainly consider the positively Z-graded polynomial ring R=F[X,Y] over an arbitrary field F and Hilbert series of finitely generated graded R-modules. The central result is an arithmetic criterion for such a series to be the Hilbert series of some R-module of positive depth. In the generic case, that is, the degrees of X and Y being coprime, this criterion can be formulated in terms of the numerical semigroup generated by those degrees.
Cite
@article{arxiv.1109.4593,
title = {Hilbert depth of graded modules over polynomial rings in two variables},
author = {Julio José Moyano-Fernández and Jan Uliczka},
journal= {arXiv preprint arXiv:1109.4593},
year = {2012}
}
Comments
28 pages