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arXiv · 1109.4593

Hilbert depth of graded modules over polynomial rings in two variables

Julio José Moyano-Fernández·Jan Uliczka
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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.

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Julio José Moyano-Fernández, Jan Uliczka. 2012-08-01. Hilbert depth of graded modules over polynomial rings in two variables. https://arxiv.org/abs/1109.4593

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