Ultraquadrics associated to affine and projective automorphims
Identificadores
Enlace permanente (URI): http://hdl.handle.net/10017/23477ISSN: 0938-1279
ESSN: 1432-0622
Editor
Springer
Fecha de publicación
2014Patrocinadores
Ministerio de Ciencia e Innovación
Cita bibliográfica
Tomás Recio, Luis F. Tabera, J. Rafael Sendra, CarlosVillarino. "Ultraquadrics associated to affine and projective automorphims". Appicable Algebra in Engineering, Communication and Computing (2014) 25: 431-445.
Palabras clave
Ultraquadrics
Field automorphisms
Rational parametrization
Optimal reparameterization
Proyectos
info:eu-repo/grantAgreement/MICINN//MTM2011-25816-C02-01/ES/ALGORITMOS Y APLICACIONES EN GEOMETRIA DE CURVAS Y SUPERFICIES/
Tipo de documento
info:eu-repo/semantics/article
Versión
info:eu-repo/semantics/acceptedVersion
Versión del editor
http://dx.doi.org/10.1007/s00200-014-0236-1Derechos
(c) Springer-Verlag Berlin Heildelberg 2014
Derechos de acceso
info:eu-repo/semantics/openAccess
Resumen
The concept of ultraquadric has been introduced by the authors as a tool to algorithmically solve the problem of simplifying the coefficients of a given rational parametrization in K(α)(t1, . . . , tn) of an algebraic variety of arbitrary dimension over a field extension K(α). In this context, previous work in the one-dimensional case has shown the importance of mastering the geometry of 1-dimensional ultraquadrics (hypercircles). In this paper we study, for the first time, the properties of some higher dimensional ultraquadrics, namely, those associated to automorphisms in the field K(α)(t1, . . . , tn), defined by linear rational (with common denominator) or by polynomial (with inverse also polynomial) coordinates. We conclude, among many other observations, 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. We conclude with some further details about the real-complex, 2-dimensional case, showing, for instance, that this family of ultraquadrics can be presented as a collection of ruled surfaces described by pairs of hypercircles.
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