Liaison and Cohen–Macaulayness conditions

Using liaison, we study projective curves which are close to complete intersections in terms of Castelnuovo–Mumford regularity or degree and we obtain conditions for a space curve C being arithmetically Cohen–Macaulay, generalizing a result of E. D. Davis. These conditions apply also, in weaker forms, to equidimensional and lCM subschemes of codimension two and to curves in ℙ^n , with n ≥ 4. The results for curves are sharp as suitable examples show.