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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

[1] F. Pauer, “Closure of $\mathrm{SL}_2$-orbits in projective spaces”, Manuscripta Math., 87:3 (1995), 295–309 | DOI | MR | Zbl

[2] V. L. Popov, “Struktura zamykanii orbit v prostranstvakh konechnomernykh lineinykh predstavlenii gruppy $\mathrm{SL}_2$”, Matem. zametki, 16:6 (1974), 943–950 | MR | Zbl

[3] Kh. Kraft, Geometricheskie metody v teorii invariantov, Mir, M., 1987 | MR | Zbl

[4] E. B. Vinberg, “Slozhnost deistvii reduktivnykh grupp”, Funkts. analiz i ego pril., 20:1 (1986), 1–13 | MR | Zbl

[5] B. Sturmfels, Gröbner Bases and Convex Polytopes, University Lecture Series, 8, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl