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Invariants and separating morphisms for algebraic group actions

Dufresne, Emilie; Kraft, Hanspeter

Authors

Emilie Dufresne

Hanspeter Kraft



Abstract

The first part of this paper is a refinement of Winkelmann’s work on invariant rings and quotients of algebraic group actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient X//G given by the possibly not finitely generated ring of invariants is “almost” an algebraic variety, and that the quotient morphism π: X → X//G has a number of nice properties. One of the main difficulties comes from the fact that the quotient morphism is not necessarily surjective. These general results are then refined for actions of the additive group Ga, where we can say much more. We get a rather explicit description of the so-called plinth variety and of the separating variety, which measures how much orbits are separated by invariants. The most complete results are obtained for representations. We also give a complete and detailed analysis of Roberts’ famous example of a an action of Ga on 7-dimensional affine space with a non-finitely generated ring of invariants.

Journal Article Type Article
Publication Date Jun 30, 2015
Journal Mathematische Zeitschrift
Print ISSN 0025-5874
Electronic ISSN 1432-1823
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 280
Issue 1-2
APA6 Citation Dufresne, E., & Kraft, H. (2015). Invariants and separating morphisms for algebraic group actions. Mathematische Zeitschrift, 280(1-2), https://doi.org/10.1007/s00209-015-1420-0
DOI https://doi.org/10.1007/s00209-015-1420-0
Publisher URL https://link.springer.com/article/10.1007%2Fs00209-015-1420-0
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at link.springer.com via http://dx.doi.org/10.1007/s00209-015-1420-0.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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