Projection of a nonsingular plane quintic curve and the dihedral group of order eight
نویسنده
چکیده
Let C be a nonsingular plane quintic curve over the complex number field C, and let πP : C → P be a projection from P ∈ C. Let LP be the Galois closure of the field extension C(C)/C(P) induced by πP , where C(C) and C(P) are the rational function fields of C and P, respectively. We call the point P a D4-point if the Galois group of LP /C(P) is isomorphic to the dihedral group D4 of order eight. In this paper, we prove that the number of D4-points for C equals 0, 1, 3, 5, or 15, and show that the curve with 15 D4-points is projectively equivalent to the Fermat quintic curve.
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