Families of Galois closure curves for plane quartic curves

Yoshihara, Hisao

J. Math. Kyoto Univ., Tome 43 (2003) no. 4, p. 651-659 / Harvested from Project Euclid

Résumé

For a smooth quartic plane curve $C$ we show an existence of a family of Galois closure curves $\phi : S \longrightarrow C$, where $S$ is a nonsingular projective surface and $\phi ^{-1}(P)$ is isomorphic to the Galois closure curve $C_{P}$ for a general point $P \in C$. Moreover we determine the types of singular fibers. As a corollary we can say that $C_{P}$ is not isomorphic to $C_{Q}$ if $P$ is close to $Q$.

Publié le : 2003-05-15
Classification: 14H50

@article{1250283700,
     author = {Yoshihara, Hisao},
     title = {Families of Galois closure curves for plane quartic curves},
     journal = {J. Math. Kyoto Univ.},
     volume = {43},
     number = {4},
     year = {2003},
     pages = { 651-659},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250283700}
}

Yoshihara, Hisao. Families of Galois closure curves for plane quartic curves. J. Math. Kyoto Univ., Tome 43 (2003) no. 4, pp.  651-659. http://gdmltest.u-ga.fr/item/1250283700/