Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 1, pp. 241-260 (2005)

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On $F_{q^2}$-maximal curves of genus $\mathbf{\frac{1}{6}(q-3)q}$

Miriam Abdón and Fernando Torres

Dep. Matemática, PUC-Rio, Marquês de S. Vicente 225, 22453-900, Rio de Janeiro, RJ, Brazil, e-mail:; IMECC-UNICAMP, Cx. P. 6065, Campinas, 13083-970-SP, Brazil e-mail:

Abstract: We show that an $\fq$-maximal curve of genus $\frac{1}{6}(q-3)q>0$ is either a non-reflexive space curve of degree $q+1$ whose tangent surface is also non-reflexive, or it is uniquely determined, up to isomorphism, by a plane model of Artin-Schreier type whenever $ q\geq 27$.

Keywords: finite field, maximal curve, non-reflexive variety, Artin-Schreier extension, additive polynomial

Classification (MSC2000): 11G20; 14G05, 14G10

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Electronic version published on: 11 Mar 2005. This page was last modified: 4 May 2006.

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