Lecture at Politecnico di Milano on 20 November, 2003

title : Families of Galois closure curves for plane quartic curves

the abstract

 For a smooth quartic plane curve C we show an existence of a family of Galois closure curves
f : S ---> C, where S is a nonsingular projective surface and a fiber f^{-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.