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Actions of compact groups on coherent sheaves

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Abstract

We consider actions of compact real Lie GroupsK on complex spacesX such that the associated reducedK-space admits a semistable quotient, e.g.X is a Stein space. We show that there is a complex spaceX cendowed with a holomorphic action of the universal complexificationG ofK that containsX as an openK-stable subset. As our main result, we prove that every coherentK-sheaf onX extends uniquely to a holomorphicG-sheaf onX c.

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Authors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Konstanz, 78457, Konstanz, Germany

    J. Hausen

  2. Department of Mathematics, Brandeis University, 02254-9110, Waltham, MA, USA

    P. Heinzner

Authors
  1. J. Hausen
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  2. P. Heinzner
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Supported by a Heisenberg Stipendium of the Deutsche Forschungsgemeinschaft.

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Hausen, J., Heinzner, P. Actions of compact groups on coherent sheaves. Transformation Groups 4, 25–34 (1999). https://doi.org/10.1007/BF01236660

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  • DOI: https://doi.org/10.1007/BF01236660

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