English

On Lower Bounds for $s$-multiplicities

Commutative Algebra 2017-08-22 v1

Abstract

A recent continuous family of multiplicity functions on local rings was introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz multiplicities. The obvious goal is to use this as a tool for deforming results from one to the other. The values in this family which do not match these classic variants however are not known yet to be well-behaved. This article explores lower bounds for these intermediate multiplicities as well as gives evidence for analogies of the Watanabe-Yoshida minimality conjectures for unmixed singular rings.

Keywords

Cite

@article{arxiv.1708.06273,
  title  = {On Lower Bounds for $s$-multiplicities},
  author = {Lance Edward Miller and William D. Taylor},
  journal= {arXiv preprint arXiv:1708.06273},
  year   = {2017}
}

Comments

10 pages

R2 v1 2026-06-22T21:19:40.923Z