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arXiv · 1708.06273

On Lower Bounds for $s$-multiplicities

Lance Edward Miller·William D. Taylor
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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.

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Lance Edward Miller, William D. Taylor. 2017-08-21. On Lower Bounds for $s$-multiplicities. https://arxiv.org/abs/1708.06273

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