2005/06/06 by Josef Schicho, Schicho, Josef
Computer Science · Engineering · Mathematics · #14E08 #14E30 #14G05 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #math.AG #msc:14E08 #msc:14E30 #msc:14G05
paper · pdf · doi:10.48550/arxiv.math/0506097
16 pages, 1 figure
arxiv created 2005/06/06 · openalex publication_date 2005/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The parametric degree of a rational surface is the degree of the polynomials in the smallest possible proper parametrization. An example shows that the parametric degree is not a geometric but an arithmetic concept, in the sense that it depends on the choice of the ground field. In this paper, we introduce two geometrical invariants of a rational surface, namely level and keel. These two numbers govern the parametric degree in the sense that there exist linear upper and lower bounds.