English

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.

Keywords

Cite

@article{arxiv.1311.6047,
  title  = {Irrational behavior of algebraic discrete valuations},
  author = {Soumya D. Sanyal},
  journal= {arXiv preprint arXiv:1311.6047},
  year   = {2014}
}
R2 v1 2026-06-22T02:13:42.071Z