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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

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A generalization of the Giulietti–Korchmáros maximal curve

Arnaldo Garcia
  • IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brazil. Email:
/ Cem Güneri / Henning Stichtenoth
Published Online: 2010-04-12 | DOI: https://doi.org/10.1515/advgeom.2010.020


We introduce a family of algebraic curves over 𝔽q2n (for an odd n) and show that they are maximal. When n = 3, our curve coincides with the 𝔽q6-maximal curve that has been found by Giulietti and Korchmáros recently. Their curve (i.e., the case n = 3) is the first example of a maximal curve proven not to be covered by the Hermitian curve.

Received: 2008-02-14

Published Online: 2010-04-12

Published in Print: 2010-07-01

Citation Information: Advances in Geometry. Volume 10, Issue 3, Pages 427–434, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom.2010.020, April 2010

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