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arXiv · 2107.14188

The asymptotic Samuel function and invariants of singularities

A. Benito·A. Bravo·S. Encinas
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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.

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A. Benito, A. Bravo, S. Encinas. 2021-07-29. The asymptotic Samuel function and invariants of singularities. https://arxiv.org/abs/2107.14188

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