English

Quantifying singularities with differential operators

Commutative Algebra 2019-09-30 v4 Algebraic Geometry

Abstract

The FF-signature of a local ring of prime characteristic is a numerical invariant that detects many interesting properties. For example, this invariant detects (non)singularity and strong FF-regularity. However, it is very difficult to compute. Motivated by different aspects of the FF-signature, we define a numerical invariant for rings of characteristic zero or p>0p>0 that exhibits many of the useful properties of the FF-signature. We also compute many examples of this invariant, including cases where the FF-signature is not known. We also obtain a number of results on symbolic powers and Bernstein-Sato polynomials.

Keywords

Cite

@article{arxiv.1810.04476,
  title  = {Quantifying singularities with differential operators},
  author = {Holger Brenner and Jack Jeffries and Luis Núñez-Betancourt},
  journal= {arXiv preprint arXiv:1810.04476},
  year   = {2019}
}

Comments

76 pages. Comments welcome

R2 v1 2026-06-23T04:34:43.067Z