Classification of the Tor-algebras of codimension four Gorenstein local rings (Q1058556)

Let R,m,k be a Gorenstein local ring in which 2 is a unit and assume that k has square roots. Let K be a grade four Gorenstein ideal in R; and Let \(\Lambda_{\bullet}\) be the graded algebra Tor\({}^ R_{\bullet}(R/K,k)\). We prove that \(\Lambda_{\bullet}\) is a Poincaré duality algebra with one of just four possible forms for the multiplication in non-complementary degrees. In subsequent work with C. Jacobsson this result is used to demonstrate rationality of the Poincaré series \(P_{R/K}\). The main technique used is that of tight double linkage, a notion developed by the authors in earlier work, which enables one to understand the minimal free resolution of R/K in great detail.