Cyclic homology of affine hypersurfaces with isolated singularities (Q1369611)

Let \(R = K[X_{1},\cdots ,X_{n}]\) for \(K\) an algebraically closed field of characteristic \(0\) and \(A = R/(F)\) where \(F = 0\) defines a hypersurface with only isolated singularities. We let \(\Omega^{1}_{A/K}\) denote the module of Kähler differentials. Then, in terms of de Rham cohomology, the author shows that the Hodge-components of cyclic homology are given by \[ HC_{n}^{(i)}(A) =\begin{cases} T(\Omega^{N-1}_{A/K})\oplus \mathbb{H}_{dR}^{N-1}(A) & \text{if } 2i-n = N-1, \\ \mathbb{H}_{dR}^{2i-n}(A) &\text{otherwise}, \end{cases} \] where \(T(\Omega^{N-1}_{A/K})\) is the torsion part of \(\Omega^{N-1}_{A/K}\).