Set-theoretic generators of rational space curves

Abstract

We show how to calculate three low degree set-theoretic generators (i.e., algebraic surfaces) for all rational space curves of low degree (degree ≤ 6 ) as well as for all higher degree rational space curves where at least one element of their μ -basis has degree 1 from a μ -basis of the parametrization. In addition to having low degree, at least two of these surface generators are always ruled surfaces. Whenever possible we also show how to compute two set-theoretic complete intersection generators for these rational space curves from a μ -basis of their parametrization.