Über Hilberts vierzehntes Problem für Varietäten mit Kompliziertheit eins - Knop, Friedrich (Mathematische Zeitschrift, 1993)
Let G be a connected reductive group with Borel subgroup B acting on a normal variety X. The complexity of X is lowest codimension of a B-orbit. Theorem: If X is unirational (e.g. quasi-homogeneous) of complexity at most one then the ring k[X] of global functions is finitely generated. This result is sharp: If X is not unirational or of complexity at least two then k[X] might not be finitely generated.