Steps in the classification of Cohen-Macaulay modules over singularities of type \(x^t +y^3\) (Q1303797)

Let \(K\) be an algebraically closed field of characteristic \(\neq 3\) and \(i,j,t\) positive integers, \(1\leq i<j<t\) and \(i+j\neq t\). It is proved that there exists a finite number of non-isomorphic indecomposable maximal Cohen-Macaulay modules \(N\) over \(K[[x,y]]/ \langle x^t+ y^3\rangle\) such that \(N/yN\) is a direct sum of several modules of type \(K[[x]]/ \langle x^i \rangle\) and \(K[[x]]/ \langle x^j\rangle\). These modules are completely described.