Periods of generalized Fermat curves

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, we find set generators first homology group curve. Finally, with this information, period lattice associated Jacobian variety.