Regularity bounds by minimal generators and Hilbert function

We prove that the Castelnuovo-Mumford regularity of a projective C curve embedded in an n-dimensional projective space over over an algebraically closed field is bounded by the maximum among two integers, the first of which is related to the regularity of the Hilbert function of the curve itself and the second one depends on the degrees of a complete intersection properly containing the given curve. We also investigate the sharpness of this bound showing that it is achieved by curves algebraically linked to ones having degenerate hyperplane section.