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Galois points on quartic curves in characteristic 3. (English) Zbl 1134.14307
Summary: We study Galois points for a smooth plane curve \(C\subset \mathbb{P}^2\) in characteristic \(3\). If \(C\) has the separable dual map, we have \(\delta(C)+\delta'(C)\leq 1\), where \(\delta(C)\) (resp. \(\delta'(C)\)) is the number of inner (resp. outer) Galois points of \(C\). On the other hand, the condition \(\delta(C)+\delta'(C)> 1\) gives a characterization of the Fermat quartic.

MSC:
14H50 Plane and space curves
12F10 Separable extensions, Galois theory
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