On two-dimensional quasihomogeneous isolated singularities. I (Q1325230)

In the mid-eighties the author conjectured that a two-dimensional integrally closed analytic \(k\)-algebra over an algebraically closed field \(k\) of characteristic 0 is graded if and only if the module of Zariski differentials is isomorphic to the Auslander module. (The latter can be defined as the (minimal) Cohen-Macaulay approximation of the maximal ideal.) In the present paper the ``if'' part of the conjecture is proved for hypersurface rings. The ``only if'' part is shown to be always true.