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Matrix representations for toric parametrizations

Nicolás Botbol 1, 2 Alicia Dickenstein 2 Marc Dohm 3, 4, *
* Corresponding author
3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (... - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : 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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Submitted on : Tuesday, July 29, 2008 - 10:41:08 PM
Last modification on : Thursday, January 20, 2022 - 5:32:52 PM
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  • HAL Id : hal-00308281, version 1
  • ARXIV : 0807.4802


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



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