On the Cohen-Macaulay type of the general hypersurface section of a curve

Abstract

A theorem of Strano ([24]) states that if C is a reduced, irreducible curve in lP 3 lying on no quadric surface, and if a general hyperplane section C N H of C is a complete intersection, then C itself must be a complete intersection. This was extended by Re ([22]) to the case where C is a locally Cohen-Macaulay curve in lW. It was then shown by Huneke and Ulrich ([14]) that if C is reduced and connected, not lying on a quadric hypersurface, and if C A H is merely Gorenstein, then the same is true of C. Finally, the first author ([18]) extended the techniques of [14] to show that if H is replaced by a general hypersurface of degree d then similar results hold. Recall that one definition of a Gorenstein scheme is "arithmetically CohenMacaulay with Cohen-Macaulay type one." In other words, in a minimal free resolution