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, Volume 65, Issue 4, pp 385–393 | Cite as

The Picard group of a complex quotient variety

  • Dorothee Feldmüller


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.


Line Bundle Number Theory Algebraic Geometry Topological Group Spectral Sequence 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Dorothee Feldmüller
    • 1
  1. 1.Fakultät und Institut für MathematikRuhr-Universität BochumBochum 1

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