At the moment we are
woefully lacking a sufficient condition for two subschemes in Pn to be in the same
liaison class, except for the case of codimension 2. On the other hand, a theorem of
Schenzel gives a good necessary condition in any codimension < n. In this article we
first give a new proof of this theorem. We then apply this result to certain curves in
P4 by considering hyperplane sections. Specifically, if C is a collection of
t skew lines in P4, we ask when C can be linked to another set of skew
lines under the “extreme” conditions where C is degenerate and where C is
“general”.
