Maximal Cohen-Macaulay modules and Gorenstein algebras

JOURNAL OF ALGEBRA

卷:238

Article

Kleppe, JO ; Peterson, C

关键词: Gorenstein algebra;    Cohen-Macaulay algebra;    maximal Cohen-Macaulay module;    sections of modules;    conormal module;    Koszul homology;    canonical module;    strongly Cohen-Macaulay;    licci;   

DOI  :  10.1006/jabr.2000.8665

来源: Elsevier

【 摘 要 】

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, 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 contest. If M is a maximal Cohen-Macaulay B-module whose sheafified top exterior power is a twist of (K) over bar (B), and if M satisfies certain additional homoiogical 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 ail have sheafified top exterior power. equal to a twist of (K) over bar (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 mod;le within a broad family of easily manipulated maximal Cohen-Macaulay modules whose sections can be used to construct Gorenstein quotients of R. (C) 2001 Academic Press.

【 授权许可】

Free