Behavior of the fiber and the base points of parametrizations under projections
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20450DOI: 10.1007/s11786-013-0139-8
ISSN: 1661-8270
Publisher
Springer
Date
2013Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Pérez Díaz, S. & Sendra, J.R. 2013, “Behavior of the fiber and the base points of parametrizations under projections”, Mathematics in Computer Science, vol. 7, no. 2, pp. 167-184.
Keywords
Rational parametrization
Unirational variety
Degree of a rational map
Fiber of a rational map
Base points
Generalized resultants
Description / Notes
This is the author’s version of a work that was accepted for publication
in Mathematics in Computer Science.
Changes resulting from the publishing process, such as peer review,
editing, corrections, structural formatting, and other quality control
mechanisms may not be reflected in this document.
Changes may have been made to this work since it was submitted for
publication. A definitive version was subsequently published
in Mathematics in Computer Science Volume 7, Issue 2 (2013), Page
167-184 DOI 10.1007/s11786-013-0139-8
Both authors are members of the of the Research Group ASYNACS (Ref. CCEE2011/R34).
Project
info:eu-repo/grantAgreement/MICINN//MTM2008-04699-C03-01/ES/VARIEDADES PARAMETRICAS: ALGORITMOS Y APLICACIONES/
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Document type
info:eu-repo/semantics/article
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
http://dx.doi.org/10.1007/s11786-013-0139-8Rights
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
© Springer Nature, 2013
Access rights
info:eu-repo/semantics/openAccess
Abstract
Given a rational parametrization P( t ), t = (t1, . . . , tr ), of an r-dimensional unirational variety, we
analyze the behavior of the variety of the base points of P( t ) in connection to its generic fibre, when successively
eliminating the parameters ti . For this purpose. we introduce a sequence of generalized resultants whose primitive
and content parts contain the different components of the projected variety of the base points and the fibre.
In addition, when the dimension of the base points is strictly smaller than 1 (as in the well known cases of curves
and surfaces), we show that the last element in the sequence of resultants is the univariate polynomial in the corresponding
Gröbner basis of the ideal associated to the fibre; assuming that the ideal is in t1-general position and
radical.
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