Conformal Versus Topological Conjugacy of Automorphisms on Compact Riemann Surfaces

We produce a family of algebraic curves (closed Riemann surfaces)S admitting two cyclic groups H₁ and H₂ of conformal automorphisms,which are topologically (but not conformally) conjugate andsuch that S/H_i is the Riemann sphere . The relevance of thisexample is that it shows that the subvarieties of moduli spaceconsisting of points parametrizing curves which occur as cycliccoverings (of a fixed topological type) of need not be normal.1991 Mathematics Subject Classification 14H10, 30F10.