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Affine embeddings with a finite number of orbits. (English) Zbl 1010.14011
Summary: Let \(G\) be a reductive algebraic group and let \(H\) be a reductive subgroup of \(G\). We describe all pairs \((G,H)\) such that, for any affine \(G\)-variety \(X\) with a dense \(G\)-orbit isomorphic to \(G/H\), the number of \(G\)-orbits in \(X\) is finite.

MSC:
14M07 Low codimension problems in algebraic geometry
14E25 Embeddings in algebraic geometry
14L30 Group actions on varieties or schemes (quotients)
57S25 Groups acting on specific manifolds
14R20 Group actions on affine varieties
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