On the structure of Cohen-Macaulay modules over hypersurfaces of countable Cohen-Macaulay representation type

Let R be a complete local hypersurface over an algebraically closed field of characteristic different from two, and suppose that R has countable Cohen-Macaulay (CM) representation type. In this paper, it is proved that the maximal Cohen-Macaulay (MCM) R-modules which are locally free on the punctured spectrum are dominated by the MCM R-modules which are not locally free on the punctured spectrum. More precisely, there exists a single R-module X such that the indecomposable MCM R-modules not locally free on the punctured spectrum are X and its syzygy Omega X and that any other MCM R-modules are obtained from extensions of X and Omega X. (C) 2012 Elsevier Inc. All rights reserved.