On the monodromy of weierstrass points

Summary In this paper we consider the family of curves of genus g=2m with a g ₃ ¹ lying on a particular rational normal scroll S in P^g– 1(C). We define a covering of this family representing the Weierstrass points and we study the monodromy. Applying the techniques of 3] we prove that if g=4 the monodromy is the full symmetric group and for general g=2m it is transitive. We show also that the generic curve of the family has only normal Weierstrass points generalizing a classical result. We work always over the complex numbers.Partially supported by: Ministero della Pubblica Istruzione - Italia; Consiglio Nazionale delle Ricerche — Italia.