{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:49:24Z","timestamp":1776804564568,"version":"3.51.2"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"315","license":[{"start":{"date-parts":[[2019,3,15]],"date-time":"2019-03-15T00:00:00Z","timestamp":1552608000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003176","name":"Ministerio de Educaci\u00c3\u00b3n, Cultura y Deporte","doi-asserted-by":"publisher","award":["MTM2016-75980-P"],"award-info":[{"award-number":["MTM2016-75980-P"]}],"id":[{"id":"10.13039\/501100003176","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003176","name":"Ministerio de Educaci\u00c3\u00b3n, Cultura y Deporte","doi-asserted-by":"publisher","award":["MTM2013-40680-P"],"award-info":[{"award-number":["MTM2013-40680-P"]}],"id":[{"id":"10.13039\/501100003176","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Given a smooth curve defined over a field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    that admits a non-singular plane model over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k overbar\">\n                        <mml:semantics>\n                          <mml:mover>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo accent=\"false\">\n                              \u00af\n                              \n                            <\/mml:mo>\n                          <\/mml:mover>\n                          <mml:annotation encoding=\"application\/x-tex\">\\overline {k}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , a fixed separable closure of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , it does not necessarily have a non-singular plane model defined over the field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . We determine under which conditions this happens and we show an example of such phenomenon: a curve defined over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    admitting plane models but none defined over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Now, even assuming that such a smooth plane model exists, we wonder about the existence of non-singular plane models over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    for its twists. We characterize twists possessing such models and we also show an example of a twist not admitting any non-singular plane model over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . As a consequence, we get explicit equations for a non-trivial Brauer-Severi surface. Finally, we obtain a theoretical result to describe all the twists of smooth plane curves with cyclic automorphism group having a model defined over\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    whose automorphism group is generated by a diagonal matrix.\n                  <\/p>","DOI":"10.1090\/mcom\/3317","type":"journal-article","created":{"date-parts":[[2017,8,30]],"date-time":"2017-08-30T10:04:24Z","timestamp":1504087464000},"page":"421-438","source":"Crossref","is-referenced-by-count":5,"title":["On twists of smooth plane curves"],"prefix":"10.1090","volume":"88","author":[{"given":"Eslam","family":"Badr","sequence":"first","affiliation":[]},{"given":"Francesc","family":"Bars","sequence":"additional","affiliation":[]},{"given":"Elisa","family":"Lorenzo Garc\u00eda","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2018,3,15]]},"reference":[{"key":"1","unstructured":"E.Badr, On the stratification of smooth plane curves by automorphism groups. PhD thesis, September 2017, Universitat Aut\u00f2noma de Barcelona."},{"issue":"5","key":"2","doi-asserted-by":"publisher","first-page":"3605","DOI":"10.1007\/s00009-016-0705-9","article-title":"On the locus of smooth plane curves with a fixed automorphism group","volume":"13","author":"Badr, Eslam","year":"2016","journal-title":"Mediterr. J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/1660-5446","issn-type":"print"},{"issue":"10","key":"3","doi-asserted-by":"publisher","first-page":"4327","DOI":"10.1080\/00927872.2015.1087547","article-title":"Automorphism groups of nonsingular plane curves of degree 5","volume":"44","author":"Badr, Eslam","year":"2016","journal-title":"Comm. 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Poincar\u00e9","volume":"61","author":"Ch\u00e2telet, Fran\u00e7ois","year":"1944","journal-title":"Ann. Sci. \\'{E}cole Norm. Sup. (3)","ISSN":"https:\/\/id.crossref.org\/issn\/0012-9593","issn-type":"print"},{"key":"8","unstructured":"The GAP Group, GAP-Groups, Algorithms, and Programming, Version 4.5.7, 2012. (http:\/\/www.gap-system.org)"},{"issue":"2","key":"9","doi-asserted-by":"publisher","first-page":"514","DOI":"10.1016\/j.jalgebra.2005.06.022","article-title":"A Lie algebra method for rational parametrization of Severi-Brauer surfaces","volume":"303","author":"de Graaf, Willem A.","year":"2006","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"10","series-title":"Princeton Series in Applied Mathematics","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1515\/9781400847419","volume-title":"Algebraic curves over a finite field","author":"Hirschfeld, J. W. P.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780691096797"},{"key":"11","isbn-type":"print","volume-title":"Fields of moduli and fields of definition of curves","author":"Huggins, Bonnie Sakura","year":"2005","ISBN":"https:\/\/id.crossref.org\/isbn\/9780542597930"},{"key":"12","unstructured":"J. Jahnel, The Brauer-Severi Variety Associated with a Central Simple Algebra: A Survey. See \\url{https:\/\/www.math.uni-bielefeld.de\/lag\/man\/052.pdf}"},{"key":"13","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1016\/j.jalgebra.2012.07.054","article-title":"Hyperelliptic curves and their invariants: geometric, arithmetic and algorithmic aspects","volume":"372","author":"Lercier, Reynald","year":"2012","journal-title":"J. Algebra","ISSN":"https:\/\/id.crossref.org\/issn\/0021-8693","issn-type":"print"},{"key":"14","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1112\/S146115701400031X","article-title":"Parametrizing the moduli space of curves and applications to smooth plane quartics over finite fields","volume":"17","author":"Lercier, Reynald","year":"2014","journal-title":"LMS J. Comput. Math."},{"key":"15","unstructured":"E. Lorenzo, Arithmetic properties of non-hyperelliptic genus 3 curves. PhD dissertation, Universitat Polit\u00e8cnica de Catalunya (2015), Barcelona."},{"issue":"1","key":"16","doi-asserted-by":"publisher","first-page":"169","DOI":"10.4171\/RMI\/931","article-title":"Twists of non-hyperelliptic curves","volume":"33","author":"Lorenzo Garc\u00eda, Elisa","year":"2017","journal-title":"Rev. Mat. Iberoam.","ISSN":"https:\/\/id.crossref.org\/issn\/0213-2230","issn-type":"print"},{"issue":"5","key":"17","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.ffa.2010.06.001","article-title":"Twists of genus three curves over finite fields","volume":"16","author":"Meagher, Stephen","year":"2010","journal-title":"Finite Fields Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/1071-5797","issn-type":"print"},{"key":"18","unstructured":"R. Pannekoek, On the parametrization over \u211a of cubic surfaces. Master dissertation, May 2009, University of Groningen."},{"key":"19","unstructured":"J. Ro\u00e9, X. Xarles, Galois descent for the gonality of curves, Arxiv:1405.5991v3, 2015. To appear in Math. Res. Lett."},{"key":"20","unstructured":"E. Tengan, Central Simple Algebras and the Brauer group, XVII Latin American Algebra Colloquium, (2009). See the book in http:\/\/www.icmc.usp.br\/ etengan\/algebra\/arquivos\/cft.pdf"},{"key":"21","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1934-7","volume-title":"Introduction to cyclotomic fields","volume":"83","author":"Washington, Lawrence C.","year":"1997","ISBN":"https:\/\/id.crossref.org\/isbn\/0387947620","edition":"2"},{"issue":"2","key":"22","doi-asserted-by":"publisher","first-page":"129","DOI":"10.2307\/1989011","article-title":"On division algebras","volume":"22","author":"Wedderburn, J. H. M.","year":"1921","journal-title":"Trans. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9947","issn-type":"print"},{"key":"23","doi-asserted-by":"publisher","first-page":"509","DOI":"10.2307\/2372670","article-title":"The field of definition of a variety","volume":"78","author":"Weil, Andr\u00e9","year":"1956","journal-title":"Amer. J. 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