Let $C$ be a smooth plane quartic curve defined over a field $k$ and $k(C)$ the rational function field of $C$. Let $\pi_P$ be the projection from $C$ to a line $\ell$ with a center $P\in C$. Then $\pi_P$ induces an extension of fields; $k(C)/k(\ell)$. Let $\widetilde C$ be a nonsingular model of the Galois closure of the extension, which we call the Galois closure curve of $k(C)/k(\ell)$. We give an answer to the problem for the genus of the Galois closure curve of quartic curve.
Publié le : 2008-03-15
Classification:
Galois point,
genus,
quartic curve,
14H45,
14H05
@article{1207580347,
author = {Watanabe, S.},
title = {The genera of Galois closure curves for plane quartic curves},
journal = {Hiroshima Math. J.},
volume = {38},
number = {1},
year = {2008},
pages = { 125-134},
language = {en},
url = {http://dml.mathdoc.fr/item/1207580347}
}
Watanabe, S. The genera of Galois closure curves for plane quartic curves. Hiroshima Math. J., Tome 38 (2008) no. 1, pp. 125-134. http://gdmltest.u-ga.fr/item/1207580347/