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

Producció científica: Capítol de llibre › Contribució a congrés/conferència › Avaluat per experts

1 Citació (Scopus)

Resum

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	Anglès
Títol de la publicació	Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020
Editors	A Mantzaflaris
Lloc de publicació	New York
Editor	Association for Computing Machinery
Pàgines	107-113
Nombre de pàgines	7
ISBN (electrònic)	978-1-4503-7100-1
DOIs	https://doi.org/10.1145/3373207.3404039
Estat de la publicació	Publicada - 2020
Publicat externament	Sí
Esdeveniment	45th International Symposium on Symbolic and Algebraic Computation - Durada: 20 de jul. 2020 → 23 de jul. 2020

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Conferència	45th International Symposium on Symbolic and Algebraic Computation
Període	20/07/20 → 23/07/20

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10.1145/3373207.3404039

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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.",

keywords = "Quillen-Suslin Theorem, Effective bounds, Mu-bases, Parametrization, Syzygies",

author = "Teresa Cortadellas and Carlos D'Andrea and \{Eulalia Montoro\}, M.",

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note = "45th International Symposium on Symbolic and Algebraic Computation ; Conference date: 20-07-2020 Through 23-07-2020",

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Cortadellas, T, D'Andrea, C & Eulalia Montoro, M 2020, Bounds for Degrees of Minimal μ-bases of Parametric Surfaces. in A Mantzaflaris (ed.), Proceedings Of The 45th International Symposium On Symbolic And Algebraic Computation, Issac 2020. Association for Computing Machinery, New York, pàg. 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. pàg. 107-113.

Producció científica: Capítol de llibre › Contribució a congrés/conferència › Avaluat per experts

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T1 - Bounds for Degrees of Minimal μ-bases of Parametric Surfaces

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AU - Eulalia Montoro, M.

PY - 2020

Y1 - 2020

N2 - 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.

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.

KW - Quillen-Suslin Theorem

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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