Minimal generators of the defining ideal of the Rees Algebra associated to monoid parameterizations

Teresa Cortadellas Benitez; Carlos D'Andrea

doi:10.1016/j.cagd.2010.04.003

Minimal generators of the defining ideal of the Rees Algebra associated to monoid parameterizations

Teresa Cortadellas Benitez
, Carlos D'Andrea

Producció científica: Article en revista indexada › Article › Avaluat per experts

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Resum

We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parameterizations having a syzygy of minimal degree (mu = 1). We also show that our approach can be applied to parameterizations of rational surfaces having a Hilbert-Burch resolution with mu(1) = mu(2) = 1.

Idioma original	Anglès
Pàgines (de-a)	461-473
Nombre de pàgines	13
Revista	Computer Aided Geometric Design
Volum	27
Número	6
DOIs	https://doi.org/10.1016/j.cagd.2010.04.003
Estat de la publicació	Publicada - d’ag. 2010
Publicat externament	Sí

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10.1016/j.cagd.2010.04.003

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abstract = "We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parameterizations having a syzygy of minimal degree (mu = 1). We also show that our approach can be applied to parameterizations of rational surfaces having a Hilbert-Burch resolution with mu(1) = mu(2) = 1. ",

keywords = "Local complete intersection surfaces, Monoid parametrizations, Rees Algebra",

author = "\{Cortadellas Benitez\}, Teresa and Carlos D'Andrea",

year = "2010",

month = aug,

doi = "10.1016/j.cagd.2010.04.003",

language = "English",

volume = "27",

pages = "461--473",

journal = "Computer Aided Geometric Design",

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AU - D'Andrea, Carlos

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N2 - We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parameterizations having a syzygy of minimal degree (mu = 1). We also show that our approach can be applied to parameterizations of rational surfaces having a Hilbert-Burch resolution with mu(1) = mu(2) = 1.

AB - We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parameterizations having a syzygy of minimal degree (mu = 1). We also show that our approach can be applied to parameterizations of rational surfaces having a Hilbert-Burch resolution with mu(1) = mu(2) = 1.

KW - Local complete intersection surfaces

KW - Monoid parametrizations

KW - Rees Algebra

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JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

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ER -

Minimal generators of the defining ideal of the Rees Algebra associated to monoid parameterizations

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