Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems - Burban, Igor, 1977-; Drozd, Yurij A. (Memoirs of the American Mathematical Society, 2017)
In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of \mathbb{k}[[x, y, z]]/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated singulari.