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Cocharacter-closure and the rational Hilbert-Mumford Theorem
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Publication details
| Journal | Mathematische Zeitschrift |
|---|---|
| Date | Accepted/In press - 3 Oct 2016 |
| Date | E-pub ahead of print - 10 Nov 2016 |
| Date | Published (current) - 10 Nov 2017 |
| Issue number | 1-2 |
| Volume | 287 |
| Number of pages | 34 |
| Pages (from-to) | 39-72 |
| Early online date | 10/11/16 |
| Original language | English |
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.
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.
Bibliographical note
© Authors, 2016
- Affine G-variety, Cocharacter-closed orbit, Rationality
Research areas
Projects
New perspectives on Buildings, Geometric Invariant Theory and Algebraic Groups
Project: Research project (funded) › Research
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