The asymptotic Samuel functions and applications to resolution of singularities techniques
Commutative Algebra
2025-07-11 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2506.14993,
title = {The asymptotic Samuel functions and applications to resolution of singularities techniques},
author = {A. Benito and A. Bravo and S. Encinas},
journal= {arXiv preprint arXiv:2506.14993},
year = {2025}
}
Comments
38 pages. The abstract has ben modified