The classification of homogeneous Cohen-Macaulay rings of finite representation type | Zendy

David Eisenbud | Zendy; J�rgen Herzog | Zendy

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The classification of homogeneous Cohen-Macaulay rings of finite representation type

Author(s) -

David Eisenbud,

J�rgen Herzog

Publication year - 1988

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/bf01456058

Subject(s) - mathematics , type (biology) , homogeneous , pure mathematics , representation (politics) , algebra over a field , combinatorics , ecology , biology , politics , political science , law

In this paper we classify the homogeneous Cohen-Macaulay rings which are of finite representation type, that is, the Cohen-Macaulay rings which are positively graded and generated in degree 1, with an algebraically closed field of characteristic 0 in degree 0, and which have, up to isomorphisms and shifts in the grading, only a finite number of indecomposable maximal Cohen-Macaulay modules (MCM-modules). Our main contribution is to show that a homogeneous Cohen-Macaulay ring of finite representation type and dimension >__ 2 must have "minimal multiplicity". Putting this together with previous results of Auslander, Auslander-Reiten, Buchweitz-Greuel-Schreyer, Greuel-Kn6rrer, and Solberg, we obtain:

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