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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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Volume 13, Issue 2


The automorphism group of the generalized Giulietti–Korchmáros function field

Cem Güneri / Mehmet Özdemiry / Henning Stichtenoth
Published Online: 2013-03-29 | DOI: https://doi.org/10.1515/advgeom-2012-0040


The Giulietti-Korchmáros (GK) function field is the first example of a maximal function field which is not a subfield of the Hermitian function field over the same constant field. The generalized GK function field Cn was later introduced by Garcia, Güneri and Stichtenoth and was shown to be maximal too. In the present article we determine the automorphism group of the generalized GK function field. We prove that all the automorphisms of Cn fix the unique rational place at infinity and they are exactly the lifts of automorphisms of the Hermitian subfield Hn ⊂ Cn which fix the infinite place of Hn

Keywords: Algebraic curves; algebraic function fields; maximal curves; maximal function fields; automorphisms of function fields

About the article

The authors are supported by TÜBITAK project 111T234. The author is supported by a scholarship through the TÜBITAK project 107T897 during the writing of this manuscript.

Published Online: 2013-03-29

Published in Print: 2013-04-01

Citation Information: Advances in Geometry, Volume 13, Issue 2, Pages 369–380, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2012-0040.

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