Rational plane curves parameterizable by conics

TL;DR

This paper introduces rational plane curves parameterizable by conics, extending known classes, and characterizes their parameterizations and algebraic properties.

Contribution

It extends the class of parameterizable curves from lines to conics and describes their parameterizations and algebraic structure.

Findings

They are images of monoid curves via quadratic transformations.

All proper parameterizations of these curves are described.

A set of minimal generators of the Rees Algebra is provided.

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.