The Asymptotic Samuel Function of a Filtration
Commutative Algebra
2022-11-24 v1 Algebraic Geometry
Abstract
We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study the notion of projective equivalence of filtrations and the relation between the asymptotic Samuel function and the multiplicity of a filtration. We further consider the case of discrete valued filtrations and show that they have particularly nice properties.
Keywords
Cite
@article{arxiv.2211.13205,
title = {The Asymptotic Samuel Function of a Filtration},
author = {Steven Dale Cutkosky and Smita Praharaj},
journal= {arXiv preprint arXiv:2211.13205},
year = {2022}
}
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21 pages