Equivalence problem and automorphism groups of certain compact Riemann surfaces

Let V be the compact Riemann surface defined by the equation: Vn=f(x), where n is a positive integer and f is a rational function of x. For such V, there is a conjecture: CONJECTRE: The moduli of such V can be determined by the branch locus of the map (υV)∈V→x∈P. ..