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Mathematics of Computation

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Computing the singularities of rational surfaces


Authors: S. Pérez-Díaz, J. R. Sendra and C. Villarino
Journal: Math. Comp. 84 (2015), 1991-2021
MSC (2010): Primary 14Q10; Secondary 14J17, 68W30
DOI: https://doi.org/10.1090/S0025-5718-2014-02907-4
Published electronically: October 9, 2014
MathSciNet review: 3335901
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Abstract: Given a rational projective parametrization $ \mathcal {P}(\mathfrak{s},\mathfrak{t},\mathfrak{v})$ of a rational projective surface $ \mathcal {S}$ we present an algorithm such that, with the exception of a finite set (maybe empty) $ \mathfrak{B}$ of projective base points of $ \mathcal {P}$, decomposes the projective parameter plane as $ {\mathbb{P}}^2(\mathbb{K})\setminus \mathfrak{B}=\bigcup _{k=1}^{\ell } \mathfrak{S}_k$ such that, if $ (\mathfrak{s}_0:\mathfrak{t}_0:\mathfrak{v}_0)\in \mathfrak{S}_k$, then $ \mathcal {P}(\mathfrak{s}_0,\mathfrak{t}_0,\mathfrak{v}_0)$ is a point of $ \mathcal {S}$ of multiplicity $ k$.


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Additional Information

S. Pérez-Díaz
Affiliation: Dpto. de Física y Matemáticas, Universidad de Alcalá, E-28871 Madrid, Spain
Email: sonia.perez@uah.es

J. R. Sendra
Affiliation: Dpto. de Física y Matemáticas, Universidad de Alcalá, E-28871 Madrid, Spain
Email: rafael.sendra@uah.es

C. Villarino
Affiliation: Dpto. de Física y Matemáticas, Universidad de Alcalá, E-28871 Madrid, Spain
Email: carlos.villarino@uah.es

DOI: https://doi.org/10.1090/S0025-5718-2014-02907-4
Received by editor(s): December 25, 2011
Received by editor(s) in revised form: January 23, 2013, June 5, 2013, and October 27, 2013
Published electronically: October 9, 2014
Additional Notes: This work was partially supported by the Spanish Ministerio de Ciencia e Innovación under the project MTM2008-04699-C03-01 and by the Ministerio de Economía y Competitividad under the project MTM2011-25816-C02-01; the authors are members of the Research Group ASYNACS (Ref. CCEE2011/R34).
Article copyright: © Copyright 2014 American Mathematical Society

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