

In this talk we will consider the graded polynomial ring R=F[X,Y] over an arbitrary field F and Hilbert series of finitely generated graded R-modules. We will explain the notion of Hilbert depth, emphasizing the positively graded case. In particular, we give an arithmetic criterion for such a series to be the Hilbert series of some positively graded R-module of positive depth. Furthermore, we will show some bridges between this criterion and numerical semigroups. This is a joint work with Jan Uliczka.
