On the Base Point Locus of Surface Parametrizations: Formulas and Consequences

• Published in: Communications in mathematics and statistics Vol. 10; no. 4; pp. 757 - 783
• Main Authors: Cox, David A., Pérez-Díaz, Sonia, Sendra, J. Rafael
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022; Springer Nature B.V
• Subjects: Loci; Mathematics; Mathematics and Statistics; Parameterization; Statistics; Base point; 14J29; 14Q10; Hilbert–Samuel multiplicity; Surface parametrization; Reparametrization; 14J70; Surface degree; Parametrization degree

This paper shows that the multiplicity of the base point 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 pa...