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:
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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.
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(1)
R has a finite Buchsbaum-representation type, that is R possesses only finitely many isomorphism classes of indecomposable maximal Buchsbaum R modules.
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(2)
e(R) = 1 and v (R) ≦ 3.
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(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.
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(1)
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© 1989 Springer-Verlag New York Inc.
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Goto, S. (1989). Surface Singularities of Finite Buchsbaum-Representation Type. In: Hochster, M., Huneke, C., Sally, J.D. (eds) Commutative Algebra. Mathematical Sciences Research Institute Publications, vol 15. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3660-3_12
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DOI: https://doi.org/10.1007/978-1-4612-3660-3_12
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