Abstract
For a field k, let G be a reductive kgroup and V an affine kvariety on which G acts. Using the notion of cocharacterclosed G(k)orbits in V , we prove a rational version of the celebrated HilbertMumford 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 cocharacterclosure and to highlight how it differs from the usual Zariskiclosure.
Original language  English 

Pages (fromto)  3972 
Number of pages  34 
Journal  Mathematische Zeitschrift 
Volume  287 
Issue number  12 
Early online date  10 Nov 2016 
DOIs  
Publication status  Published  Oct 2017 
Keywords
 math.AG
 math.GR
 20G15, 14L24
 Affine Gvariety
 Cocharacterclosed orbit
 Rationality
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Profiles

Ben Martin
 School of Natural & Computing Sciences, Mathematical Science  Personal Chair
 Mathematical Sciences (Research Theme)
Person: Academic