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

作　　者：David A.Cox Sonia Pérez-Díaz J.Rafael Sendra 

机构地区：[1]Department of Mathematics and Statistics,Amherst College,Amherst,MA 01002,USA [2]Universidad de Alcalá,Dpto.de Física y Matemáticas,28871 Madrid,Spain

出　　处：《Communications in Mathematics and Statistics》2022年第4期757-783,共27页数学与统计通讯（英文）

基　　金：partially supported by FEDER/Ministerio de Ciencia,Innovación y Universidades-Agencia Estatal de Investigación/MTM2017-88796-P(Symbolic Computation:new challenges in Algebra and Geometry together with its applications)。

摘　　要：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 parametrization,the base point 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.

关 键 词：Base point Hilbert-Samuel multiplicity Surface parametrization Reparametrization Parametrization degree Surface degree 

分 类 号：O17[理学—数学]