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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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