Ramification points of double coverings of curves and Weierstrass points

Summary Let π: X→C be a double covering with X smooth curve and C elliptic curve. Let R(π)⊂X be the ramification locus of π. Every P∈R(π) is a Weierstrass point of X and we study the triples (C, π, X) for which the set of corresponding Weierstrass points have certain semigroups of non-gaps. We study the same problem also for triple cyclic coverings of C. Entrata in Redazione il 17 luglio 1998. The authors were partially supported by MURST and GNSAGA of CNR (Italy).