Quantifying singularities with differential operators
Commutative Algebra
2019-09-30 v4 Algebraic Geometry
Abstract
The -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 -regularity. However, it is very difficult to compute. Motivated by different aspects of the -signature, we define a numerical invariant for rings of characteristic zero or that exhibits many of the useful properties of the -signature. We also compute many examples of this invariant, including cases where the -signature is not known. We also obtain a number of results on symbolic powers and Bernstein-Sato polynomials.
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