Maximal Cohen-Macaulay modules and the quasihomogeneity of isolated Cohen-Macaulay singularities

Abstract

We conjecture that a complete isolated Cohen-Macaulay singularity of dimension ≥ 2 \geq 2 is graded if and only if sufficiently high syzygy modules of the residue field and of the transpose of the module of Kähler differentials are isomorphic. The "only if" part of the conjecture is proved for hypersurface singularities.