Regularity bounds for curves by minimal generators and Hilbert function
Abstract
Let
ρ
C
be the regularity of the Hilbert function of a projective curve
C
in
P
n
K
over an algebraically closed field
K
and
α
1
,...,
α
n−1
be minimal degrees for which there exists a complete intersection of type
(
α
1
,...,
α
n−1
)
containing the curve
C
. Then the Castelnuovo-Mumford regularity of
C
is upper bounded by
max{
ρ
C
+1,
α
1
+...+
α
n−1
−(n−2)}
. We study and, for space curves, refine the above bound providing several examples.