Quantifying singularities with differential operators
arXiv:1810.04476
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.
76 pages. Comments welcome