Let k , n ? 2 be integers. A generalized Fermat curve of type ( ) is a compact Riemann surface S that admits subgroup conformal automorphisms H ? Aut isomorphic to Z such the quotient / biholomorphic sphere C ˆ and has + 1 branch points, each one order . There exists good algebraic model for these objects, which makes them easier study. Using tools from topology integration theory on surfaces, ...