Cocharacter-closure and the rational Hilbert-Mumford Theorem

Michael Bate, Sebastian Herpel, Benjamin Martin, Gerhard Roehrle

Research output: Contribution to journalArticle

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For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V , we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. A number of examples are discussed to illustrate the concept of cocharacter-closure and to highlight how it differs from the usual Zariski-closure.
Original languageEnglish
Pages (from-to)39-72
Number of pages34
JournalMathematische Zeitschrift
Issue number1-2
Early online date10 Nov 2016
Publication statusPublished - Oct 2017


  • math.AG
  • math.GR
  • 20G15, 14L24
  • Affine G-variety
  • Cocharacter-closed orbit
  • Rationality

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