Details
| Original language | English |
|---|---|
| Pages (from-to) | 1957-1997 |
| Number of pages | 41 |
| Journal | Mathematics of Computation |
| Volume | 90 |
| Issue number | 330 |
| Early online date | 22 Mar 2021 |
| Publication status | Published - Jul 2021 |
Abstract
Keywords
- math.AG, 14B05, 32S25
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Algebra and Number Theory
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In: Mathematics of Computation, Vol. 90, No. 330, 07.2021, p. 1957-1997.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Embedded desingularization for arithmetic surfaces
T2 - toward a parallel implementation
AU - Frühbis-Krüger, Anne
AU - Ristau, Lukas
AU - Schober, Bernd
N1 - Funding Information: Received by the editor February 12, 2020, and, in revised form, September 28, 2020, and November 30, 2020. 2020 Mathematics Subject Classification. Primary 14E15; Secondary 14B05, 14J17, 13P99. 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”.
PY - 2021/7
Y1 - 2021/7
N2 - We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based onwork by Cossart-Jannsen-Saito, though our variant uses a refinement of theorder instead of the Hilbert-Samuel function as a measure for the complexityof the singularity. We particularly focus on aspects arising when working inmixed characteristics. Furthermore, we exploit the algorithm’s natural parallel structure rephrasing it in terms of Petri nets for use in the parallelizationenvironment GPI-Space with SINGULAR as computational back-end.
AB - We present an algorithmic embedded desingularization of arithmetic surfaces bearing in mind implementability. Our algorithm is based onwork by Cossart-Jannsen-Saito, though our variant uses a refinement of theorder instead of the Hilbert-Samuel function as a measure for the complexityof the singularity. We particularly focus on aspects arising when working inmixed characteristics. Furthermore, we exploit the algorithm’s natural parallel structure rephrasing it in terms of Petri nets for use in the parallelizationenvironment GPI-Space with SINGULAR as computational back-end.
KW - math.AG
KW - 14B05, 32S25
UR - http://www.scopus.com/inward/record.url?scp=85107625561&partnerID=8YFLogxK
U2 - 10.1090/mcom/3624
DO - 10.1090/mcom/3624
M3 - Article
VL - 90
SP - 1957
EP - 1997
JO - Mathematics of Computation
JF - Mathematics of Computation
SN - 0025-5718
IS - 330
ER -