L2 d-bar cohomology groups of some singular complex spaces
arXiv:1101.1860
Abstract
Let X be a pure n-dimensional (n>1) complex analytic set in C^N with an isolated singularity at 0. In this paper we express the L2-(0,q)-d-bar-cohomology groups for all q with 0<q<n+1, of a sufficiently small deleted neighborhood of the singular point, in terms of resolution data. We also obtain identifications of the L2-(0,q)-d-bar-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.
v2:revised and expanded; dropped irreducibility condition on Theorems 1.1 and 1.2, added a lemma to make the proof of Corollary 1.5 more self-contained, added Corollary 1.6 and a new section to treat the case q=n and elaborated on the vanishing or not of H^{0,dim_x X-1}_{(2)}(U') in the last example of section 7.1