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 .
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