Maximal Cohen-Macaulay Modules and Gorenstein Algebras

Jan O. Kleppe and Chris Peterson

Let B be a graded Cohen-Macaulay quotient of a Gorenstein ring, R. It is known that sections of the dual of the canonocal module, K_B, 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 K^~_B and if M satisfies additional homological conditions then regular sections of M* can again be used to construct Gorenstein quotients of R. On Cohen-Macaulay quotients, the normal bundle, the first Koszul homological module and several other associated modules all have sheafified top exterior power equal to a twist of K^~_B It 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 Cohen-Macaulay modules whose sections can be used to construct Gorenstein of R.