Matrix representations for toric parametrizations |
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Authors: | Nicol s Botbol, Alicia Dickenstein,Marc Dohm |
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Affiliation: | aDepartamento de Matemática, FCEN, Universidad de Buenos Aires, Ciudad Universitaria, Pab.I, 1428 Buenos Aires, Argentina;bInstitut de Mathématiques de Jussieu, Université de P. et M. Curie, Paris VI, France;cLaboratoire J. A. Dieudonné, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 2, France |
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Abstract: | In this paper we show that a surface in parametrized over a 2-dimensional toric variety can be represented by a matrix of linear syzygies if the base points are finite in number and form locally a complete intersection. This constitutes a direct generalization of the corresponding result over established in [Busé, L., Jouanolou, J.-P., 2003. J. Algebra 265 (1), 312–357] and [Busé, L., Chardin, M.J., 2005. Symbolic Comput. 40 (4–5), 1150–1168]. Exploiting the sparse structure of the parametrization, we obtain significantly smaller matrices than in the homogeneous case and the method becomes applicable to parametrizations for which it previously failed. We also treat the important case in detail and give numerous examples. |
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Keywords: | Matrix representation Rational surface Syzygy Approximation complex Implicitization Toric variety |
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