Surface Singularities of Finite Buchsbaum-Representation Type

Abstract

The purpose of this paper is to determine the structure of surface singularities of finite Buchsbaum-representation type and the main results are summarized into the following: Let R be a Noetherian complete local ring of dim R = 2 and assume that the residue class field of R is algebraically closed. Let e(R) and v (R) denote, respectively, the multiplicity and the embedding dimension of R. Then the following three conditions are equivalent. (1) R has a finite Buchsbaum-representation type, that is R possesses only finitely many isomorphism classes of indecomposable maximal Buchsbaum R modules. (2) e(R) = 1 and v (R) ≦ 3. (3) R ≅ P/XI where P is a three-dimensional complete regular local ring with maximal ideal n, X ∈ n\ n 2 and I is an ideal of P such that ht P I ≧ 2. KeywordsExact SequenceLocal RingMaximal IdealIsomorphism ClassNormal RingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.