Almost universal parametrizations for cubic surfaces Original Research Article

Universal parametrizations have been developed as an useful tool for working with rational surfaces. For example, they allow the systematic classification of rational curves with low degree on the surface and can be used for interpolation problems. Unfortunately, it is conjectured, that not every rational surface has a universal parametrization. To make the advantages usable for more surfaces, we introduce “almost universal parametrizations” as a generalization of universal parametrizations. We present them exemplarily for a special class of cubic surfaces, which do probably not possess a universal parametrization, and show applications.