Embedded desingularization for arithmetic surfaces -- toward a parallel implementation
Algebraic Geometry
2020-09-29 v3
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 {\sc Singular} as computational back-end.
Cite
@article{arxiv.1712.08131,
title = {Embedded desingularization for arithmetic surfaces -- toward a parallel implementation},
author = {Anne Fruehbis-Krueger and Lukas Ristau and Bernd Schober},
journal= {arXiv preprint arXiv:1712.08131},
year = {2020}
}
Comments
32 pages; reworked the algorithm to determine the interesting primes and made minor changes throughout the preprint