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Cohen-Macaulay modules on hypersurface singularities. II. (English) Zbl 0617.14034
This is the subsequent paper of H. Knörrer’s paper with the same title [see the preceding review]. The main object is to prove the converse of Knörrer’s result, namely that a non-simple hypersurface singularity R is of infinite Cohen-Macaulay-representation type, i.e. there are infinitely many isomorphism classes of indecomposable maximal Cohen- Macaulay modules (MCM) over R (see theorem A and B). Moreover the authors classify those (non-isolated) hypersurface singularities \((A_{\infty}\) and \(D_{\infty})\) which are of countable CM-representation type (see theorem B).
An application to vector bundles on projective hypersurfaces with ”no cohomology in the middle” is given (see theorem C).
Reviewer: M.Herrmann

MSC:
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14J17 Singularities of surfaces or higher-dimensional varieties
14B05 Singularities in algebraic geometry
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