The asymptotic Samuel function and invariants of singularities

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.

37 pages. Some hypotheses used in the proof of Proposition 2.10 but not explicitly stated have been added.To appear in Rev. Mat. Complutense

References in corpus (4)

• Singularities in positive characteristic, stratification and simplification of the singular locus
• Techniques for the study of singularities with applications to resolution of 2-dimensional schemes
• Rees algebras and resolution of singularities
• Nash multiplicity sequences and Hironaka's order function