On the points of Weierstrass in dimensions greater than one

In this paper, the classical concept of Weierstrass points on a Riemann surface is generalized to the consideration of similar points associated with a holomorphic vector bundle E over a compact complex manifold M. These points are invariants of the pair (E, M). The study of these general Weierstrass points is then initiated in this paper by deriving some results about the relationship of the points to singular sets of holomorphic mappings of the manifold to Grassmann spaces associated with the vector space of sections of the vector bundle. The accessibility of the point sets are demonstrated with some examples.