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Article Dans Une Revue Computer Aided Geometric Design Année : 2009

Matrix representations for toric parametrizations

Résumé

In this paper we show that a surface in P^3 parametrized over a 2-dimensional toric variety T 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 P^2 established in [BJ03] and [BC05]. 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 T = P^1 x P^1 in detail and give numerous examples.
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Dates et versions

hal-00308281 , version 1 (29-07-2008)

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Nicolás Botbol, Alicia Dickenstein, Marc André Dohm. Matrix representations for toric parametrizations. Computer Aided Geometric Design, 2009, 26 (7), pp.757-771. ⟨hal-00308281⟩
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