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Matematicheskie Zametki, 2007, Volume 81, Issue 5, Pages 766–775
DOI: https://doi.org/10.4213/mzm3719 (Mi mzm3719) 		 
On the Finiteness of the Number of Orbits on Quasihomogeneous $(\mathbb C^*)^k\times SL_2(\mathbb C)$-manifolds

E. V. Sharoiko

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm3719
Abstract: 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, orbit, character lattice, Borel subgroup, analytic curve, irreducible algebraic variety.
Received: 03.11.2005
Revised: 30.08.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 5, Pages 686–694
DOI: https://doi.org/10.1134/S000143460705015X
Bibliographic databases:
UDC: 512.743.7
Language: Russian
Citation: E. V. Sharoiko, “On the Finiteness of the Number of Orbits on Quasihomogeneous $(\mathbb C^*)^k\times SL_2(\mathbb C)$-manifolds”, Mat. Zametki, 81:5 (2007), 766–775; Math. Notes, 81:5 (2007), 686–694
Citation in format AMSBIB
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