Galois points for a plane curve in characteristic two |
| |
Authors: | Satoru Fukasawa |
| |
Affiliation: | Department of Mathematical Sciences, Faculty of Science, Yamagata University, Kojirakawa-machi 1-4-12, Yamagata 990-8560, Japan |
| |
Abstract: | 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 δ′(C) the number of Galois points contained in P2?C. In this article we will present two results with respect to determination of δ′(C) in characteristic two. First we determine δ′(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 δ′(C). Second we determine δ′(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. |
| |
Keywords: | 14H50 12F10 14H05 |
本文献已被 ScienceDirect 等数据库收录! |
|