Characterization of polynomial surfaces of revolution and polynomial quadrics
Algebraic Geometry
2025-01-22 v1
Abstract
In this paper, we characterize the polynomiality of surfaces of revolution by means of the polynomiality of an associated plane curve. In addition, if the surface of revolution is polynomial, we provide formulas for computing a polynomial parametrization, over , of the surface. Furthermore, we perform the first steps towards the analysis of the existence, and actual computation, of real polynomial parametrizations of surfaces of revolution. As a consequence, we give a complete picture of the real polynomiality of quadrics and we formulate a conjecture for the general case.
Keywords
Cite
@article{arxiv.2501.11976,
title = {Characterization of polynomial surfaces of revolution and polynomial quadrics},
author = {Michal Bizzarri and Miroslav Lávička and J. Rafael Sendra and Jan Vršek},
journal= {arXiv preprint arXiv:2501.11976},
year = {2025}
}