On the theorem of Castelnuovo for Buchsbaum curves (Q908980)

Castelnuovo proved that for a smooth reduced irreducible curve \(C\subset {\mathbb{P}}^ 3\) of degree \( d,\) the surfaces of degree \( n\) trace out a complete linear system on C for all \(n\geq d-2\). This paper improves this bound for Buchsbaum curves by involving the invariant \(e(C):=\max \{t| \quad H^ 1{\mathcal O}_ C(t)\neq 0\}\) into the bound.