Rational plane curves parameterizable by conics

Teresa Cortadellas Benítez; Carlos D'Andrea

doi:10.1016/j.jalgebra.2012.09.034

Rational plane curves parameterizable by conics

Teresa Cortadellas Benítez
, Carlos D'Andrea^*

^*Corresponding author for this work

Research output: Indexed journal article › Article › peer-review

12 Citations (Scopus)

Abstract

We introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines (also known as monoid curves). We show that they are the image of monoid curves via suitable quadratic transformations in projective plane. We also describe all the possible proper parameterizations of them, and a set of minimal generators of the Rees Algebra associated to these parameterizations, extending well-known results for curves parameterizable by lines.

Original language	English
Pages (from-to)	453-480
Number of pages	28
Journal	Journal of Algebra
Volume	373
DOIs	https://doi.org/10.1016/j.jalgebra.2012.09.034
Publication status	Published - 1 Jan 2013
Externally published	Yes

Keywords

Implicitization
Monoid curves
Parameterizations
Primary
Rational plane curves
Rees Algebra
Secondary
Singularities

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10.1016/j.jalgebra.2012.09.034Licence: Other

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AB - We introduce the class of rational plane curves parameterizable by conics as an extension of the family of curves parameterizable by lines (also known as monoid curves). We show that they are the image of monoid curves via suitable quadratic transformations in projective plane. We also describe all the possible proper parameterizations of them, and a set of minimal generators of the Rees Algebra associated to these parameterizations, extending well-known results for curves parameterizable by lines.

KW - Implicitization

KW - Monoid curves

KW - Parameterizations

KW - Primary

KW - Rational plane curves

KW - Rees Algebra

KW - Secondary

KW - Singularities

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Rational plane curves parameterizable by conics

Abstract

Keywords

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