Birational reparameterizations of surfaces

Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parameterization with empty base locus, and the input parameterization...

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Bibliographic Details
Published in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024-07, Vol.118 (3), Article 109
Main Authors: Caravantes, Jorge, Pérez-Díaz, Sonia, Sendra, J. Rafael
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Parameterization
Theoretical
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Summary:Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational parameterization with empty base locus, and the input parameterization is transversal, the degree of the solution is determined in advance and the dimension of the space of solutions is reduced. As a consequence, for these cases, we present a second faster algorithm.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-024-01609-9