Curves Having Schemes of Special Linear Systems with Multiple Components

Abstract

In this article, we show that it is of frequent occurrence that smooth curves do have multiple components for some of their schemes of special divisors. For a smooth space curve C of degree d, we give sufficient conditions implying that has a multiple component, and we prove the existence of many space curves satisfying those conditions. As an example of a more general result for curves in ℙ r , we prove that general complete intersection curves of degree d in ℙ4 do have multiple components for the schemes and .