The monodromy of Weierstrass points

Abstract

We show that the monodromy of the family of curves (Riemann surfaces) acts as the full symmetric group on the Weierstrass points of a general curve. The proof uses a degeneration to certain reducible curves, and the theory of limit series developed in our (1986, 1987a, b). Some of the monodromy is actually constructed by fixing a (reducible) curve and varying its “canonical” series.