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The Picard group of a complex quotient variety

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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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Authors and Affiliations

  1. Fakultät und Institut für Mathematik, Ruhr-Universität Bochum, Universitätsstr. 150, D-4630, Bochum 1

    Dorothee Feldmüller

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  1. Dorothee Feldmüller
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Feldmüller, D. The Picard group of a complex quotient variety. Manuscripta Math 65, 385–393 (1989). https://doi.org/10.1007/BF01172787

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  • DOI: https://doi.org/10.1007/BF01172787

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