Linkage theory for algebras with pure resolutions (Q1081648)

Let \(S=[k[X_ 1,...,X_ n]/I\) be a graded Cohen-Macaulay ring with k an infinite field. This pleasantly written paper proves that if S is generically a complete intersection and the minimal free resolution of S is pure and almost linear, then S is not in the linkage class of a complete intersection (apart from the known exceptions when S has codimension two, or S is Gorenstein of codimension three). When S has small codimension, more is said. For example, if S has codimension three and has a pure resolution, then S is the linkage class of a complete intersection if and only if S is Gorenstein. Results concerning what sequences of twists and Betti numbers can occur in minimal homogeneous resolutions of graded Cohen-Macaulay algebras are also given.