Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

Teresa Cortadellas; Carlos D'Andrea; M. Eulalia Montoro

doi:10.1145/3373207.3404039

Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

Teresa Cortadellas
, Carlos D'Andrea
, M. Eulalia Montoro

Producción científica: Capítulo del libro › Contribución a congreso/conferencia › revisión exhaustiva

1 Cita (Scopus)

Resumen

By adapting the effective version of Quillen-Suslin Theorem given in [8], we show that if the ideal defining a rational parametrization of degree d of an algebraic surface in 3-dimensional space is radical and has D points, then a mu-basis of this parametrization can be found of degree bounded by 5 max(1, D - 1)(4)(2d + 1)(4). This bound improves those obtained recently in [4] in our setup, and it is also sensitive to the number of base points.

Idioma original	Inglés
Título de la publicación alojada	Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020
Editores	A Mantzaflaris
Lugar de publicación	New York
Editorial	Association for Computing Machinery
Páginas	107-113
Número de páginas	7
ISBN (versión digital)	978-1-4503-7100-1
DOI	https://doi.org/10.1145/3373207.3404039
Estado	Publicada - 2020
Publicado de forma externa	Sí
Evento	45th International Symposium on Symbolic and Algebraic Computation - Duración: 20 jul 2020 → 23 jul 2020

Conferencia

Conferencia	45th International Symposium on Symbolic and Algebraic Computation
Período	20/07/20 → 23/07/20

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title = "Bounds for Degrees of Minimal μ-bases of Parametric Surfaces",

abstract = "By adapting the effective version of Quillen-Suslin Theorem given in [8], we show that if the ideal defining a rational parametrization of degree d of an algebraic surface in 3-dimensional space is radical and has D points, then a mu-basis of this parametrization can be found of degree bounded by 5 max(1, D - 1)(4)(2d + 1)(4). This bound improves those obtained recently in [4] in our setup, and it is also sensitive to the number of base points.",

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Cortadellas, T, D'Andrea, C & Eulalia Montoro, M 2020, Bounds for Degrees of Minimal μ-bases of Parametric Surfaces. En A Mantzaflaris (ed.), Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020. Association for Computing Machinery, New York, pp. 107-113, 45th International Symposium on Symbolic and Algebraic Computation, 20/07/20. https://doi.org/10.1145/3373207.3404039

Bounds for Degrees of Minimal μ-bases of Parametric Surfaces. / Cortadellas, Teresa; D'Andrea, Carlos; Eulalia Montoro, M.
Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020. ed. / A Mantzaflaris. New York: Association for Computing Machinery, 2020. p. 107-113.

Producción científica: Capítulo del libro › Contribución a congreso/conferencia › revisión exhaustiva

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AB - By adapting the effective version of Quillen-Suslin Theorem given in [8], we show that if the ideal defining a rational parametrization of degree d of an algebraic surface in 3-dimensional space is radical and has D points, then a mu-basis of this parametrization can be found of degree bounded by 5 max(1, D - 1)(4)(2d + 1)(4). This bound improves those obtained recently in [4] in our setup, and it is also sensitive to the number of base points.

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KW - Effective bounds

KW - Mu-bases

KW - Parametrization

KW - Syzygies

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Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

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