arXiv subjects

A. Benito

Publications and source records attributed to A. Benito.

2 recordsLinked to original sources

arXiv2025

The asymptotic Samuel functions and applications to resolution of singularities techniques

We use the asymptotic Samuel function to define the Samuel slope of a Noetherian local ring, and we prove that it characterizes regularity in the case of local excellent rings. In addition, we introduce a second invariant that refines the Samuel slope using generic linear cuts, the refined Samuel slope. We show that both, the Samuel slope and the refined Samuel slope, are connected to invariants coming from resolution of singularities.

math.AC↗

arXiv2023

The asymptotic Samuel function and invariants of singularities

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.

math.AC↗