Some bounds for the number of coincidences of morphisms between closed riemann surfaces

We give some bounds for the number of coincidences of two morphisms between given compact Riemann surfaces (complete complex algebraic curves) which generalize well known facts about the number of fixed points of automorphisms. In the particular case in which both surfaces are hyperelliptic, our results permit us to obtain a bound for the number of morphisms between them. The proof relies on the idea, first used by Schwarz in the case of automorphisms, of representing a morphism by its action on the set of Weierstrass points.