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manuscripta mathematica

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

The Picard group of a complex quotient variety

  • Dorothee Feldmüller
Article
  • 65 Downloads

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.

Keywords

Line Bundle Number Theory Algebraic Geometry Topological Group Spectral Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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