Minimal generators of the defining ideal of the Rees Algebra associated to a rational plane parameterization with \mu=2

TL;DR

This paper identifies minimal generators for the defining ideal of the Rees Algebra linked to a rational plane curve parametrization with a specific syzygy degree, advancing algebraic understanding of such curves.

Contribution

It provides explicit minimal generators for the Rees Algebra's defining ideal in the case where the syzygy degree is 2, a case not fully characterized before.

Findings

Explicit minimal generators for the ideal are constructed.

The work clarifies the algebraic structure of the Rees Algebra for these curves.

It enhances understanding of the algebraic properties of rational plane curves with =2.

Abstract

We exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated to the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2.