Ultraquadrics associated to affine and projective automorphims

Authors
Recio, Tomás; Sendra Pons, Juan RafaelUniversity of Alcalá Author; Tabera, Luis Felipe; Villarino Cabellos, CarlosUniversity of Alcalá Author
Identifiers
Permanent link (URI): http://hdl.handle.net/10017/20455
DOI: 10.1007/s00200-014-0236-1
ISSN: 0938-1279
ISBN: 9788469706510
Publisher
Springer
Date
2014
Affiliation
Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Funders
Ministerio de Ciencia e Innovación
Bibliographic citation
Appicable Algebra in Engineering Communication and Computing, 2014, v.25, p.431-455
Encuentros de Álgebra Computacional y Aplicaciones, Barcelona, 2014, p.147-150
Keywords
Ultraquadrics
Parametrization
Polynomial automorphims
Rational parametrization
Field automorphisms
Optimal reparameterization
Description / Notes
J. R. Sendra and C. Villarino are members of the research group ASYNACS (Ref. CCEE2011/R34).
Project
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
info:eu-repo/semantics/bookPart
Version
info:eu-repo/semantics/acceptedVersion
Publisher's version
http://www.ub.edu/eaca2014/2014_EACA_Conference_Proceedings.pdfhttp://dx.doi.org/10.1007/s00200-014-0236-1
Rights
© Springer, 2014
Access rights
info:eu-repo/semantics/openAccess
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Abstract
In this extended abstract, we study the properties of ultraquadrics associated with automorphisms of the field K(\alpha )(t1, . . . , tn), defined by linear rational (with common denominator) or by polynomial (with polynomial inverse) coordinates. We conclude that ultraquadrics related to polynomial automorphisms can be characterized as varieties K−isomorphic to linear varieties, while ultraquadrics arising from projective automorphisms are isomorphic to the Segre embedding of a blowup of the projective space along an ideal and, in some general case, linearly isomorphic to a toric variety. This information helps us to compute a parametrization of some ultraquadrics.
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