Degrees of Generators of Ideals Defining Subschemes of Projective Space<P>

Heath Martin, Juan Migliore, S. Nollet<P>

For an arithmetically Cohen--Macaulay subscheme
of projective space, there is a well-known bound for the 
highest degree of a minimal generator for the defining
ideal of the subscheme, in terms of the Hilbert function.  We
prove a natural extension of this bound for arbitrary locally
Cohen--Macaulay subschemes.  We then specialize to curves in
$\pthree$, and show that the curves whose defining ideal
have  generators of maximal degree satisfy an interesting
cohomological property.  The even liaison classes possessing
such curves are characterized, and we show that within an
even liaison class, all curves with the property satisfy
a strong Lazarsfeld--Rao structure theorem.  This allows us
to give relatively complete conditions for when a liaison
class contains curves whose ideals have maximal degree generators,
and where within the liaison class they occur.