Infinity branches and asymptotic analysis of algebraic space curves: New techniques and applications

Let C represent an irreducible algebraic space curve defined by the real polynomials fi(x1, x2, x3) for i = 1,2. It is a recognized fact that a birational relationship invariably exists between the points on C and those on an associated irreducible plane curve, denoted as Cp. In this work, we levera...

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Detalles Bibliográficos
Autores: Pérez Díaz, Sonia|||0000-0002-0174-5325, Wang, Xin-Yu, Magdalena Benedicto, J. Rafael, Shen, Li-Yong
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/68220
Acceso en línea:http://hdl.handle.net/10017/68220
https://dx.doi.org/10.1016/j.cagd.2025.102422
Access Level:acceso abierto
Palabra clave:Algebraic space curve
Implicit representation
Perfect curves
Infinity branches
Asymptotes
Matemáticas
Mathematics
Descripción
Sumario:Let C represent an irreducible algebraic space curve defined by the real polynomials fi(x1, x2, x3) for i = 1,2. It is a recognized fact that a birational relationship invariably exists between the points on C and those on an associated irreducible plane curve, denoted as Cp. In this work, we leverage this established relationship to delineate the asymptotic behavior of C by examining the asymptotes of Cp. Building on this foundation, we introduce a novel and practical algorithm designed to efficiently compute the asymptotes of C, given that the asymptotes of Cp have been ascertained.