First steps towards radical parametrization of algebraic surfaces

We introduce the notion of radical parametrization of a surface, and we provide algorithms to compute such type of parametrizations for families of surfaces, like: Fermat surfaces, surfaces with a high multiplicity (at least the degree minus 4) singularity, all irreducible surfaces of degree at most 5, all irreducible singular surfaces of degree 6, and surfaces containing a pencil of low-genus curves. In addition, we prove that radical parametrizations are preserved under certain type of geometric constructions that include offset and conchoids.

► We introduce the notion of radical parametrization of a surface. ► We provide algorithms to compute such parametrizations for certain families of surfaces. ► We show how to parametrize among others all irreducible surfaces of degree at most 5 and all irreducible singular surfaces of degree 6. ► We show how to parametrize surfaces containing a pencil of low-genus curves. ► We prove that radical parametrizations are preserved under certain type of geometric constructions that include offset and conchoids.