L 2-overline{partial}-Cohomology groups of some singular complex spaces

Let X be a pure n-dimensional (where n≥2) complex analytic subset in ? ^N with an isolated singularity at 0. In this paper we express the L ²-(0,q)- $overline{partial}$ -cohomology groups for all q with 1≤q≤n of a sufficiently small deleted neighborhood of the singular point in terms of resolution data. We also obtain identifications of the L ²-(0,q)- $overline{partial}$ -cohomology groups of the smooth points of X, in terms of resolution data, when X is either compact or an open relatively compact complex analytic subset of a reduced complex space with finitely many isolated singularities.