Irrational behavior of algebraic discrete valuations
Commutative Algebra
2014-06-11 v2
Abstract
We study algebraic discrete valuations dominating normal local domains of dimension two. We construct a family of examples to show that the Hilbert-Samuel function of the associated graded ring of the valuation can fail to be asymptotically of the form: quasi-polynomial plus a bounded function. We also show that the associated multiplicity can be irrational, or even transcendental.
Cite
@article{arxiv.1311.6047,
title = {Irrational behavior of algebraic discrete valuations},
author = {Soumya D. Sanyal},
journal= {arXiv preprint arXiv:1311.6047},
year = {2014}
}