Abstract
We study the structure of function fields of plane curves following our method developed previously (K. Miura and H. Yoshihara, 2000, J. Algebra226, 283–294). Let K be the function field of a smooth plane curve C of degree d (≥4) and let KP be a maximal rational subfield of K for P∈P2. We study the field extension K/KP from a geometrical viewpoint. Especially, we give a sufficient condition that the Galois group of the Galois closure of K/KP becomes a full symmetric group.
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