Abstract
For a holomorphic action of a reductive complex Lie groupG on a Stein complex spaceX the map onto the categorical quotientX//G induces a mapPic(X//G)→Pic(X) between the groups of holomorphic line bundles. Sufficient conditions are given for the injectivity of this map. The results are gained from a consideration of the relations between the cohomology rings (with values in ℤ) ofX andX//G via Leray spectral sequence.
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