2020/08/18 by David A. Cox, Cox, David A., Sonia Pérez-Dı́az +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Robotic Mechanisms and Dynamics
paper · pdf · doi:10.48550/arxiv.2008.08009
openalex publication_date 2020/08/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
This paper shows that the multiplicity of the base points locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant. As a consequence, we get a new proof of the degree formula relating the degree of the surface, the degree of the parametrization, the base points multiplicity, and the degree of the rational map induced by the parametrization. In addition, we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related. As an application of these results, we explore how the degree of a surface reparametrization is affected by the presence of base points.