Geodesic
On the Finiteness of the Number of Orbits on Quasihomogeneous $(\mathbb C^*)^k\times SL_2(\mathbb C)$-manifolds
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 766-775.

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We obtain an effective criterion for the finiteness of the number of orbits contained in the closure of a given $G$-orbit for the case of a rational linear action of the group $G:=(\mathbb C^*)^k\times SL_2(\mathbb C)$ on a finite-dimensional linear space as well as on the projectivization of such a space.
Keywords: the group $SL_2(\mathbb C)$, rational linear action, character lattice, Borel subgroup, analytic curve, irreducible algebraic variety.
Mots-clés : orbit 
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E. V. Sharoiko. On the Finiteness of the Number of Orbits on Quasihomogeneous $(\mathbb C^*)^k\times SL_2(\mathbb C)$-manifolds. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 766-775. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a14/

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