Projection of a nonsingular plane quintic curve and the dihedral group of order eight
Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 39-61.

Let C be a nonsingular plane quintic curve over the complex number field , and let π P :C 1 be a projection from PC. Let L P be the Galois closure of the field extension (C)/( 1 ) induced by π P , where (C) and ( 1 ) are the rational function fields of C and 1 , respectively. We call the point P a D 4 -point if the Galois group of L P /( 1 ) is isomorphic to the dihedral group D 4 of order eight. In this paper, we prove that the number of D 4 -points for C equals 0, 1, 3, 5, or 15, and show that the curve with 15 D 4 -points is projectively equivalent to the Fermat quintic curve.

DOI : 10.4171/RSMUP/135-3
Classification : 14
Mots-clés : Galois group of a projection, plane quintic curve, the dihedral group of order eight
Takahashi, Takeshi 1

1 Niigata University, NIIGATA, JAPAN
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     title = {Projection of a nonsingular plane quintic curve and the dihedral group of order eight},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {39--61},
     publisher = {European Mathematical Society Publishing House},
     address = {Zuerich, Switzerland},
     volume = {135},
     year = {2016},
     doi = {10.4171/RSMUP/135-3},
     url = {http://www.numdam.org/articles/10.4171/RSMUP/135-3/}
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Takahashi, Takeshi. Projection of a nonsingular plane quintic curve and the dihedral group of order eight. Rendiconti del Seminario Matematico della Università di Padova, Tome 135 (2016), pp. 39-61. doi : 10.4171/RSMUP/135-3. http://www.numdam.org/articles/10.4171/RSMUP/135-3/

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