Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies

Laurent Busé 1 Marc Dohm 1, 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
2 JAD - Laboratoire Jean Alexandre Dieudonné
Abstract : We show that the implicit equation of a surface in 3-dimensional projective space parametrized by bi-homogeneous polynomials of bi-degree (d,d), for a given positive integer d, can be represented and computed from the linear syzygies of its parametrization if the base points are isolated and form locally a complete intersection.
Keywords : implicitization linear syzygies approximation complexes
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Conference papers
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Laurent Busé, Marc Dohm. Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies. International Conference on Symbolic and Algebraic Computation (ISSAC), Jul 2007, Waterloo, Ontario, Canada. pp.69-76, ⟨10.1145/1277548.1277559⟩. ⟨inria-00168956⟩

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