On two-dimensional quasihomogeneous isolated singularities. II (Q1325231)

[For part I see \textit{A. Martsinkovsky}, ibid. 550-555 (1992; Zbl 0792.14003).] This article deals with the following conjecture of Auslander: An analytic two-dimensional isolated singularity \((R,{\mathfrak m},k)\) is quasihomogeneous if and only if the Auslander-module \(A\) of this singularity is isomorphic to the module of Zariski differentials. -- Recall that the Auslander-module is the unique non-trivial extension of the maximal ideal \({\mathfrak m}\) by the canonical module of \(R\), while the module of Zariski differentials is the bi-dual \(D_ K(R)^{**}\) of the module \(D_ K(R)\) of Kähler differentials. In this paper it is shown that the following conditions are equivalent: (a) \(R\) is quasihomogeneous; (b) The natural homomorphism \(D_ K(R)\otimes K\to D_ K(R)^{**} \otimes K\) is injective, and \(D_ K(R)^{**} \cong A\).