Resumen de On branched covering of compact Riemann surfaces with automorphisms

Gustavo Labbe Morales

• 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.