Quantifying singularities with differential operators

Autor(en): Brenner, Holger 
Jeffries, Jack
Nunez-Betancourt, Luis
Stichwörter: BERNSTEIN-SATO POLYNOMIALS; COHOMOLOGY; D-modules; EQUIVALENCE; F-SIGNATURE; GROBNER BASES; IDEALS; LOG CANONICITY; Mathematics; MODULES; Numerical invariants; PURITY; REGULAR LOCAL-RINGS; Rings of invariants; Singularities
Erscheinungsdatum: 2019
Herausgeber: ACADEMIC PRESS INC ELSEVIER SCIENCE
Journal: ADVANCES IN MATHEMATICS
Volumen: 358
Zusammenfassung: 
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. (C) 2019 Elsevier Inc. All rights reserved.
ISSN: 00018708
DOI: 10.1016/j.aim.2019.106843

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