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 language | English |
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Pages (from-to) | 39-72 |
Number of pages | 34 |
Journal | Mathematische Zeitschrift |
Volume | 287 |
Issue number | 1-2 |
Early online date | 10 Nov 2016 |
DOIs | |
Publication status | Published - 1 Oct 2017 |
Keywords
- Affine G-variety
- Cocharacter-closed orbit
- Rationality
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Ben Martin
- School of Natural & Computing Sciences, Mathematical Science - Personal Chair
Person: Academic