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...
| Autores: | , , , |
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| 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 |
| 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. |
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