Divisorial filtrations of ideals in a normal excellent local ring R can be understood as the sections of \(-nD\) where D is an effective divisor on a projective scheme X over \(\mbox{Spec}(R)\). The Rees algebra (Section Ring) of the filtration is often not noetherian. In spite of this, it's hilbert function does have some polynomial like behaviour. We discuss some good asymptotic properties of the Hilbert function, and some examples exhibiting more erratic behaviour.
