The Rees Algebra of Parametric Curves via liftings

TL;DR

This paper investigates the defining equations of the Rees algebra associated with plane and scroll curve parametrizations, connecting various prior works to understand their algebraic structure.

Contribution

It introduces a new framework linking the defining equations of Rees algebras for different classes of parametrized curves.

Findings

Established relations between Rees algebra equations for plane and scroll curves

Extended previous work by Madsen, Kustin, Polini, and Ulrich

Provided algebraic insights into curve parametrizations

Abstract

We study the defining equations of the Rees algebra of ideals arising from curve parametrizations in the plane and in rational normal scrolls, inspired by the work of Madsen and Kustin, Polini and Ulrich. The curves are related by work of Bernardi, Gimigliano and Ida, and we use this framework to relate the defining equations.