On twists of smooth plane curves

Given a smooth curve defined over a field k that admits a non-singular plane model over k, a fixed separable closure of k, it does not necessarily have a non-singular plane model defined over the field k. We determine under which conditions this happens and we show an example of such phenomenon. Now...

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Detalles Bibliográficos
Autores: Badr, Eslam|||0000-0002-3960-7243, Bars Cortina, Francesc|||0000-0003-4779-3995, Lorenzo García, Elisa
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:240667
Acceso en línea:https://ddd.uab.cat/record/240667
https://dx.doi.org/urn:doi:10.1090/mcom/3317
Access Level:acceso abierto
Palabra clave:Non-singular plane curves
Automorphism groups
Twist
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spelling On twists of smooth plane curvesBadr, Eslam|||0000-0002-3960-7243Bars Cortina, Francesc|||0000-0003-4779-3995Lorenzo García, ElisaNon-singular plane curvesAutomorphism groupsTwistGiven a smooth curve defined over a field k that admits a non-singular plane model over k, a fixed separable closure of k, it does not necessarily have a non-singular plane model defined over the field k. We determine under which conditions this happens and we show an example of such phenomenon. Now, even assuming that such a smooth plane model exists, we wonder about the existence of non-singular plane models over k for its twists. We characterize twists possessing such models and use such characterization to improve, for the particular case of smooth plane curves, the algorithm to compute twists of non-hyperelliptic curves wrote recently down by the third author. We also show an example of a twist not admitting such non-singular plane model. As a consequence, we get explicit equations for a non-trivial Brauer-Severi surface. Finally, we obtain a theoretical result to compute all the twists of smooth plane curves with cyclic automorphism group having a k-model whose automorphism group is generated by a diagonal matrix. Some examples are also provided. 22019-01-0120192019-01-01Articlehttp://purl.org/coar/resource_type/c_6501SMURhttp://purl.org/coar/version/c_71e4c1898caa6e32info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/240667https://dx.doi.org/urn:doi:10.1090/mcom/3317reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40680-Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2406672026-06-06T12:50:31Z
dc.title.none.fl_str_mv On twists of smooth plane curves
title On twists of smooth plane curves
spellingShingle On twists of smooth plane curves
Badr, Eslam|||0000-0002-3960-7243
Non-singular plane curves
Automorphism groups
Twist
title_short On twists of smooth plane curves
title_full On twists of smooth plane curves
title_fullStr On twists of smooth plane curves
title_full_unstemmed On twists of smooth plane curves
title_sort On twists of smooth plane curves
dc.creator.none.fl_str_mv Badr, Eslam|||0000-0002-3960-7243
Bars Cortina, Francesc|||0000-0003-4779-3995
Lorenzo García, Elisa
author Badr, Eslam|||0000-0002-3960-7243
author_facet Badr, Eslam|||0000-0002-3960-7243
Bars Cortina, Francesc|||0000-0003-4779-3995
Lorenzo García, Elisa
author_role author
author2 Bars Cortina, Francesc|||0000-0003-4779-3995
Lorenzo García, Elisa
author2_role author
author
dc.subject.none.fl_str_mv Non-singular plane curves
Automorphism groups
Twist
topic Non-singular plane curves
Automorphism groups
Twist
description Given a smooth curve defined over a field k that admits a non-singular plane model over k, a fixed separable closure of k, it does not necessarily have a non-singular plane model defined over the field k. We determine under which conditions this happens and we show an example of such phenomenon. Now, even assuming that such a smooth plane model exists, we wonder about the existence of non-singular plane models over k for its twists. We characterize twists possessing such models and use such characterization to improve, for the particular case of smooth plane curves, the algorithm to compute twists of non-hyperelliptic curves wrote recently down by the third author. We also show an example of a twist not admitting such non-singular plane model. As a consequence, we get explicit equations for a non-trivial Brauer-Severi surface. Finally, we obtain a theoretical result to compute all the twists of smooth plane curves with cyclic automorphism group having a k-model whose automorphism group is generated by a diagonal matrix. Some examples are also provided.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
SMUR
http://purl.org/coar/version/c_71e4c1898caa6e32
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/240667
https://dx.doi.org/urn:doi:10.1090/mcom/3317
url https://ddd.uab.cat/record/240667
https://dx.doi.org/urn:doi:10.1090/mcom/3317
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2013-40680-P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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