Matrix representations for toric parametrizations

In this paper we show that a surface in P3 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...

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Detalles Bibliográficos
Autores principales:	Botbol, N., Dickenstein, A., Dohm, M.
Formato:	JOUR
Materias:	Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Matrix algebra
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_01678396_v26_n7_p757_Botbol
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_01678396_v26_n7_p757_Botbol
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spelling	todo:paper_01678396_v26_n7_p757_Botbol2023-10-03T15:05:24Z Matrix representations for toric parametrizations Botbol, N. Dickenstein, A. Dohm, M. Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Matrix algebra In this paper we show that a surface in P3 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 P2 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 T = P1 × P1 in detail and give numerous examples. © 2009 Elsevier B.V. All rights reserved. Fil:Dickenstein, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01678396_v26_n7_p757_Botbol
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Matrix algebra
spellingShingle	Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Matrix algebra Botbol, N. Dickenstein, A. Dohm, M. Matrix representations for toric parametrizations
topic_facet	Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Approximation complex Implicitization Matrix representation Rational surface Syzygy Toric variety Matrix algebra
description	In this paper we show that a surface in P3 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 P2 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 T = P1 × P1 in detail and give numerous examples. © 2009 Elsevier B.V. All rights reserved.
format	JOUR
author	Botbol, N. Dickenstein, A. Dohm, M.
author_facet	Botbol, N. Dickenstein, A. Dohm, M.
author_sort	Botbol, N.
title	Matrix representations for toric parametrizations
title_short	Matrix representations for toric parametrizations
title_full	Matrix representations for toric parametrizations
title_fullStr	Matrix representations for toric parametrizations
title_full_unstemmed	Matrix representations for toric parametrizations
title_sort	matrix representations for toric parametrizations
url	http://hdl.handle.net/20.500.12110/paper_01678396_v26_n7_p757_Botbol
work_keys_str_mv	AT botboln matrixrepresentationsfortoricparametrizations AT dickensteina matrixrepresentationsfortoricparametrizations AT dohmm matrixrepresentationsfortoricparametrizations
_version_	1807321857303511040

Matrix representations for toric parametrizations

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