English

First Steps Towards Radical Parametrization of Algebraic Surfaces

Symbolic Computation 2013-02-21 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1206.1456,
  title  = {First Steps Towards Radical Parametrization of Algebraic Surfaces},
  author = {J. Rafael Sendra and David Sevilla},
  journal= {arXiv preprint arXiv:1206.1456},
  year   = {2013}
}

Comments

31 pages, 7 color figures. v2: added another case of genus 1

R2 v1 2026-06-21T21:15:35.835Z