Computing the topology of a planar or space hyperelliptic curve

We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of t...

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Detalles Bibliográficos
Autores: Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710, Caravantes Tortajada, Jorge|||0000-0001-9550-2481, Díaz Toca, Gema María, Tsigaridas, Elias
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/58588
Acceso en línea:http://hdl.handle.net/10017/58588
https://dx.doi.org/10.1016/j.cagd.2020.101830
Access Level:acceso abierto
Palabra clave:Hyperelliptic curves
Topology
Birational mappings
Complexity
Algebraic curves
Matemáticas
Mathematics
Descripción
Sumario:We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose topology is easy to compute, under a birational mapping of the plane or the space. We report on a Mapleimplementation of these algorithms, and present several examples. Complexity and certification issues are also discussed.