Embedded desingularization for arithmetic surfaces – toward a parallel implementation
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- by Anne Frühbis-Krüger, Lukas Ristau and Bernd Schober;
- Math. Comp. 90 (2021), 1957-1997
- DOI: https://doi.org/10.1090/mcom/3624
- Published electronically: March 22, 2021
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Abstract:
We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based on work by Cossart-Jannsen-Saito, though our variant uses a refinement of the order instead of the Hilbert-Samuel function as a measure for the complexity of the singularity. We particularly focus on aspects arising when working in mixed characteristics. Furthermore, we exploit the algorithm’s natural parallel structure rephrasing it in terms of Petri nets for use in the parallelization environment GPI-Space with Singular as computational back-end.References
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Bibliographic Information
- Anne Frühbis-Krüger
- Affiliation: Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Address at time of publication: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
- ORCID: 0000-0001-8287-012X
- Email: anne.fruehbis-krueger@uni-oldenburg.de
- Lukas Ristau
- Affiliation: Competence Center High Performance Computing, Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
- Address at time of publication: Department of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Str., 67663 Kaiserslautern, Germany
- Email: ristau@mathematik.uni-kl.de
- Bernd Schober
- Affiliation: Institut für Algebraische Geometrie, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
- Address at time of publication: Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany
- MR Author ID: 1218416
- ORCID: 0000-0003-0315-0656
- Email: schober.math@gmail.com, bernd.schober@uni-oldenburg.de
- Received by editor(s): February 12, 2020
- Received by editor(s) in revised form: September 28, 2020, and November 30, 2020
- Published electronically: March 22, 2021
- Additional Notes: The second author was partially supported by DFG-grant SFB-TRR 195 “Symbolic Tools in Mathematics and their Application”, project II.5 “Singular: A new level of abstraction and performance”.
- © Copyright 2021 American Mathematical Society
- Journal: Math. Comp. 90 (2021), 1957-1997
- MSC (2020): Primary 14E15; Secondary 14B05, 14J17, 13P99
- DOI: https://doi.org/10.1090/mcom/3624
- MathSciNet review: 4398760