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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