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...
| Authors: | ; ; ; |
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| Format: | Article |
| Publication date: | 2020 |
| Country: | España |
| Institution: | Universidad de Alcalá (UAH) |
| Repository: | e_Buah Biblioteca Digital Universidad de Alcalá |
| Language: | English |
| OAI Identifier: | oai:ebuah.uah.es:10017/58588 |
| Online Access: | http://hdl.handle.net/10017/58588 https://dx.doi.org/10.1016/j.cagd.2020.101830 |
| Access Level: | Open access |
| Keyword: | Hyperelliptic curves Topology Birational mappings Complexity Algebraic curves Matemáticas Mathematics |
| _version_ | 1878740201338044416 |
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| author | Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710 |
| author2 | Caravantes Tortajada, Jorge|||0000-0001-9550-2481 Díaz Toca, Gema María Tsigaridas, Elias |
| author2_role | author author author |
| author_browse | Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710 Caravantes Tortajada, Jorge|||0000-0001-9550-2481 Díaz Toca, Gema María Tsigaridas, Elias |
| author_facet | Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710 Caravantes Tortajada, Jorge|||0000-0001-9550-2481 Díaz Toca, Gema María Tsigaridas, Elias |
| author_role | author |
| collection | e_Buah Biblioteca Digital Universidad de Alcalá |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_cefb7bf21a0f7d41a0ed8d44e4ee0c4e |
| institution | Universidad de Alcalá (UAH) |
| instname_str | Universidad de Alcalá (UAH) |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ebuah.uah.es:10017/58588 |
| publishDate | 2020 |
| publishDateSort | 2020 |
| publisher | Elsevier |
| publisherStr | Elsevier |
| reponame_str | e_Buah Biblioteca Digital Universidad de Alcalá |
| spelling | Computing the topology of a planar or space hyperelliptic curve Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710 Caravantes Tortajada, Jorge|||0000-0001-9550-2481 Díaz Toca, Gema María Tsigaridas, Elias Hyperelliptic curves Topology Birational mappings Complexity Algebraic curves Matemáticas Mathematics 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. Agencia Estatal de Investigación Agence Nationale de la Recherche Elsevier http://hdl.handle.net/10017/58588 https://dx.doi.org/10.1016/j.cagd.2020.101830 |
| spellingShingle | Computing the topology of a planar or space hyperelliptic curve Alcázar Arribas, Juan Gerardo|||0000-0002-1665-9710 Hyperelliptic curves Topology Birational mappings Complexity Algebraic curves Matemáticas Mathematics |
| title | Computing the topology of a planar or space hyperelliptic curve |
| title_full | Computing the topology of a planar or space hyperelliptic curve |
| title_fullStr | Computing the topology of a planar or space hyperelliptic curve |
| title_full_unstemmed | Computing the topology of a planar or space hyperelliptic curve |
| title_short | Computing the topology of a planar or space hyperelliptic curve |
| title_sort | Computing the topology of a planar or space hyperelliptic curve |
| topic | Hyperelliptic curves Topology Birational mappings Complexity Algebraic curves Matemáticas Mathematics |
| topic_facet | Hyperelliptic curves Topology Birational mappings Complexity Algebraic curves Matemáticas Mathematics |
| url | http://hdl.handle.net/10017/58588 https://dx.doi.org/10.1016/j.cagd.2020.101830 |