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arXiv · 1810.04476

Quantifying singularities with differential operators

Holger Brenner·Jack Jeffries·Luis Núñez-Betancourt
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Abstract

The $F$-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 $F$-regularity. However, it is very difficult to compute. Motivated by different aspects of the $F$-signature, we define a numerical invariant for rings of characteristic zero or $p>0$ that exhibits many of the useful properties of the $F$-signature. We also compute many examples of this invariant, including cases where the $F$-signature is not known. We also obtain a number of results on symbolic powers and Bernstein-Sato polynomials.

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Holger Brenner, Jack Jeffries, Luis Núñez-Betancourt. 2018-10-10. Quantifying singularities with differential operators. https://arxiv.org/abs/1810.04476

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