Galois points for a plane curve in characteristic two

• Autores: Satoru Fukasawa
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 2, 2014, págs. 343-353
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2013.06.006
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• Resumen

  • Let C be an irreducible plane curve. A point P in the projective plane is said to be Galois with respect to C if the function field extension induced by the projection from P is Galois.

    We denote by ���(C) the number of Galois points contained in P2 \ C. In this article we will present two results with respect to determination of ���(C) in characteristic two. First we determine ���(C) for smooth plane curves of degree a power of two. In particular, we give a new characterization of the Klein quartic in terms of ���(C). Second we determine ���(C) for a generalization of the Klein quartic, which is related to an example of Artin.Schreier curves whose automorphism group exceeds the Hurwitz bound. This curve has many Galois points.