Branched two-sheeted covers

In this paper we explore the connection between Weierstrass points of subspaces of the holomorphic differentials and the geometry of the canonical curve in PC ^g-1. In particular, we consider non-hyperelliptic Riemann surfaces with involution and the Weierstrass points of the -1 eigenspace of the holomorphic differentials. The case of coverings of a torus is considered in detail.