Cocharacter-closure and the rational Hilbert-Mumford Theorem

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JournalMathematische Zeitschrift
DateAccepted/In press - 3 Oct 2016
DateE-pub ahead of print - 10 Nov 2016
DatePublished (current) - 10 Nov 2017
Issue number1-2
Volume287
Number of pages34
Pages (from-to)39-72
Early online date10/11/16
Original languageEnglish

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.

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© Authors, 2016

    Research areas

  • Affine G-variety, Cocharacter-closed orbit, Rationality

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