Irrational behavior of algebraic discrete valuations

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] We construct a family of algebraic discrete rank 1 valuations whose associated Hilbert function cannot be written as the sum of a quasi-polynomial and a bounded function. We further show that the set of multiplicities associated to these algebraic discrete rank 1 valuations contains the interval [0, 1/8 ). In particular, the associated multiplicites can be irrational.