Maximal Cohen–Macaulay Modules and Gorenstein Algebras

Let B be a graded Cohen–Macaulay quotient of a Gorenstein ring, R. It is known that sections of the dual of the canonical module, KB, can be used to construct Gorenstein quotients of R. The purpose of this paper is to place this method of construction into a broader context. If M is a maximal Cohen–Macaulay B-module whose sheafified top exterior power is a twist of B and if M satisfies certain additional homological conditions then regular sections of M* can again be used to construct Gorenstein quotients of R. On Cohen–Macaulay quotients, the normal module, the first Koszul homology module and several other associated modules all have sheafified top exterior power equal to a twist of B. If additional restrictions are placed on the Cohen–Macaulay quotients then these modules will satisfy the required additional homological conditions. This places the canonical module within a broad family of easily manipulated maximal Cohen–Macaulay modules whose sections can be used to construct Gorenstein quotients of R.