Resumen de On branched covering of compact Riemann surfaces with automorphisms
In this work, we give an algorithm to count the different conformal equivalence classes of compact Riemann surfaces that admit a group of automorphisms isomorphic to Z/nZ, n ∊ N, and that are branched coverings ofthe Riemann sphere, with signature ((n, 0); m1 ,m2 ,m3 ), m1 ,m2,m3 ∊ N.By using the previous result, we count the different conformal equivalence classes of compact Riemann surfaces in the cases of coverings with signature ((p, 0); p, p, p), p ≥ 5 and prime, and signature ((p2, 0); p2 , p2 , p), p ≥ 3 and prime.
