On some properties of the asymptotic Samuel function

2023/07/21 by Bravo, A., Encinas, S., Guillán-Rial, J. · 1 citation
#13B22 #13H15 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.11489

Abstract

The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. Here we explore some natural properties in the context of excellent, equidimensional rings containing a field. In addition, we establish some results regarding the Samuel slope of a local ring. This is an invariant related with algorithmic resolution of singularities of algebraic varieties. Among other results, we study its behavior after certain faithfully flat extensions.

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

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