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

Autor:	Cox, David A., Pérez Díaz, Sonia, Sendra Pons, Juan Rafael
Přispěvatelé:	Universidad de Alcalá. Departamento de Física y Matemáticas. Unidad docente Matemáticas
Rok vydání:	2022
Předmět:	Statistics and Probability Base point Matemáticas Applied Mathematics Surface degree Reparametrization Parametrization degree Mathematics - Algebraic Geometry Computational Mathematics FOS: Mathematics Surface parametrization Algebraic Geometry (math.AG) Mathematics Hilbert–Samuel multiplicity
Zdroj:	e_Buah Biblioteca Digital Universidad de Alcalá instname
ISSN:	2194-671X 2194-6701
DOI:	10.1007/s40304-021-00257-4
Popis:	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. Agencia Estatal de Investigación
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::387bc4e9b41c34f8d927511b6f41f0f6 https://doi.org/10.1007/s40304-021-00257-4 Zobrazit plný text záznamu Full text from SpringerLink