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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differential symmetric signature in high dimension
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by Holger Brenner and Alessio Caminata PDF
Proc. Amer. Math. Soc. 147 (2019), 4147-4159 Request permission

Abstract:

We study the differential symmetric signature, an invariant of rings of finite type over a field, introduced in a previous work by the authors in an attempt to find a characteristic-free analogue of the F-signature. We compute the differential symmetric signature for invariant rings $k[x_1,\dots ,x_n]^G$, where $G$ is a finite small subgroup of GL$(n,k)$, and for hypersurface rings $k[x_1,\dots ,x_n]/(f)$ of dimension $\geq 3$ with an isolated singularity. In the first case, we obtain the value $1/|G|$, which coincides with the F-signature and generalizes a previous result of the authors for the two-dimensional case. In the second case, following an argument by Bruns, we obtain the value $0$, providing an example of a ring where differential symmetric signature and F-signature are different.
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Additional Information
  • Holger Brenner
  • Affiliation: Institut für Mathematik, Universität Osnabrück, Albrechtstrasse 28a, 49076 Osnabrück, Germany
  • MR Author ID: 322383
  • Email: holger.brenner@uni-osnabrueck.de
  • Alessio Caminata
  • Affiliation: Institut de Matemàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
  • MR Author ID: 1111986
  • Email: alessio.caminata@unine.ch
  • Received by editor(s): November 28, 2017
  • Received by editor(s) in revised form: October 3, 2018
  • Published electronically: June 27, 2019
  • Additional Notes: The second author was supported by European Union’s Horizon 2020 research and innovation programme under grant agreement No. 701807.
  • Communicated by: Jerzy Weyman
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4147-4159
  • MSC (2010): Primary 13A50, 13D40, 13N05
  • DOI: https://doi.org/10.1090/proc/14458
  • MathSciNet review: 4002532