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

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...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematics and statistics 2022-12, Vol.10 (4), p.757-783
Main Authors: Cox, David A., Pérez-Díaz, Sonia, Sendra, J. Rafael
Format: Article
Language:English
Subjects:
Loci
Mathematics
Mathematics and Statistics
Parameterization
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2194-6701
2194-671X
DOI:10.1007/s40304-021-00257-4