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
.
ACKNOWLEDGMENT
This work has been partially supported by the fund of Scientific Research Flanders (G.0318.16).
Notes
Communicated by S. Kleiman.