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

Abstract This paper shows that the multiplicity of base point locus a projective rational surface parametrization can be expressed as degree content univariate resultant. As consequence, we get new proof formula relating surface, parametrization, and map induced by parametrization. In addition, extend both formulas to case dominant maps plane describe how loci its reparametrizations are related. an application these results, explore reparametrization is affected presence points.