Maximal Cohen–Macaulay modules over the cone of an elliptic curve

Let R=k[Y1,Y2,Y3]/(f), f=Y13+Y23+Y33, where k is an algebraically closed field with chark≠3. Using Atiyah bundle classification over elliptic curves we describe the matrix factorizations of the graded, indecomposable reflexive R-modules, equivalently we describe explicitly the indecomposable bundles over the projective curve . Using the fact that over the completion of R every reflexive module is gradable, we obtain a description of the maximal Cohen–Macaulay modules over .