Weierstrass multiple points on algebraic curves and ramified coverings (Q1279979)

Weierstrass point theory is a basic topic in Riemann surfaces. The paper deals with a generalization of this theory to \(k\)-tuples of points. The basic result, theorem 0.1, is an existence result of a Riemann surface and \(k\)-points on it having minimal Weierstrass weight. This theorem is then used to prove a result about the nongap sequence of a Weierstrass point on a \(k\)-sheeted cover of the projective line. The paper also includes a study of a class of vector bundles on coverings of elliptic curves.