On canonical curves and osculating spaces

We study the geometry of a reduced canonical curve with a nondegenerate component. We prove that the other components are rational normal curves in a certain configuration. In addition, given a nonsingular point on a nondegenerate component, we analyze the relationship between the Weierstrass semigroup and the intersection divisors of the osculating spaces with the curve. We describe how these divisors vary and present an upper bound for their degrees. We study in detail the curves that attain this bound. (C) 2002 Elsevier Science B.V. All rights reserved.