Cocharacter-closure and the rational Hilbert-Mumford Theorem

Michael Bate, Sebastian Herpel, Benjamin Martin, Gerhard Roehrle

Research output: Contribution to journalArticle

8 Citations (Scopus)
8 Downloads (Pure)

Abstract

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
Volume287
Issue number1-2
Early online date10 Nov 2016
DOIs
Publication statusPublished - Oct 2017

Keywords

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

Fingerprint Dive into the research topics of 'Cocharacter-closure and the rational Hilbert-Mumford Theorem'. Together they form a unique fingerprint.

Cite this