Background cohomology of a non-compact Kahler G-manifold
arXiv:1203.6860
Abstract
For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G it decomposes into a sum of irreducible components, each of which appears in it with finite multiplicity. Thus equivariant Betti numbers are well defined. We study various properties of the new cohomology and prove that it satisfies a Kodaira-type vanishing theorem.
the paper is considerably rewritten, main definition is slightly changed, many mistakes and misprints are corrected and some details are added in the proofs. Several important references added