ON COHEN-MACAULAY MODULES ON SURFACE SINGULARITIES

We study Cohen-Macaulay modules over normal surface singularities. Using the method of Kahn and extending it to families of modules, we classify Cohen-Macaulay modules over cusp singularities and prove that a minimally elliptic singularity is Cohen-Macaulay tame if and only if it is either simple elliptic or cusp. As a corollary, we obtain a classification of Cohen-Macaulay modules over log-canonical surface singularities and hypersurface singularities of type T-pqr; especially they are Cohen-Macaulay tame. We also calculate the Auslander-Reiten quiver of the category of Cohen-Macaulay modules in the considered cases.