The asymptotic Samuel function and invariants of singularities

2021/07/29 by Angélica Benito, A. Bravo, Benito, A. +3 · 1 citation
Computer Science · Mathematics · #13B22 #13H15 #14E15 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2107.14188

openalex publication_date 2021/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the Samuel slope of a Noetherian local ring, and we study some of its properties. In particular, we focus on the case of a local ring at singular point of a variety, and, among other results, we prove that the Samuel slope of these rings is related to some invariants used in algorithmic resolution of singularities.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

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• The asymptotic Samuel functions and applications to resolution of singularities techniques

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