Curves algebraically uniformized by radicals

Abstract:

In this talk, I would introduce a classical problem, suggested by Enriques and resumed by Zarizki: the study of complex projective curves of genus g which admit a map on the Riemann sphere with solvable Galois group. It is well known that the generic curve of genus g > 6 is not rationally uniformized by radicals. I would explain how this problem could be generalized, introducing the concept of  curves algebraically uniformized by radicals and finally I will make a  survey of the main results in this field.