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On Hilbert’s fourteenth problem for varieties of complexity one. (Über Hilberts vierzehntes Problem für Varietäten mit Kompliziertheit eins.) (German) Zbl 0788.14042
Let $$G$$ be a reductive group and $$B$$ a Borel subgroup. The complexity $$c$$ of a $$G$$-variety $$X$$ is the codimension of a generic $$B$$-orbit. It is shown that the algebra of global functions $$k[X]$$ is finitely generated whenever $$c\leq 1$$ and $$X$$ is unirational. Examples show, that none of the conditions can be relaxed. An application to the Popov-Pommerening conjecture, concerning radical subgroups, is given.
Reviewer: F.Knop

##### MSC:
 14L30 Group actions on varieties or schemes (quotients) 13A50 Actions of groups on commutative rings; invariant theory 14L24 Geometric invariant theory 13E15 Commutative rings and modules of finite generation or presentation; number of generators
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##### References:
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