Hilbert depth of graded modules over polynomial rings in two variables

Details Hilbert depth of graded modules over polynomial rings in two variables Hilbert depth of graded modules over polynomial rings in two variables

2011-09-21

arxiv.org/abs/1109.4593v1

Mathematics

Commutative Algebra

27 pages

Scientific paper

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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