We study families of ropes of any codimension that are supported on lines. We construct suitable smooth parameter spaces and conclude that all ropes of fixed degree and genus lie in the same component of the corresponding Hilbert scheme. We show that this component is generically smooth if the genus is small enough unless the characteristic of the ground field is two and the curves under consideration have degree two. In this case the component is non-reduced.
|Number of pages||33|
|Journal||International Journal of Mathematics|
|State||Published - Aug 2006|
Bibliographical noteFunding Information:
The authors warmly thank INDAM-GNSAGA for partial support. The first author was also partially supported by a Faculty Summer Research Fellowship from the University of Kentucky.
- Hilbert scheme
- Minimal free resolution
- Normal sheaf
ASJC Scopus subject areas
- Mathematics (all)