Geodesic
On a~class of quasihomogeneous affine varieties
Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 743-758.

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We give a classification of irreducible affine algebraic varieties which are quasihomogeneous with respect to a regular action by a connected linear group of automorphisms and are such that the isotropy subgroup of a point in general position contains a maximal unipotent subgroup of the group of transformations. We find criteria for the normality and factoriality of such varieties. We compute the divisor class group and give a complete description of the orbits in such varieties. 
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È. B. Vinberg; V. L. Popov. On a~class of quasihomogeneous affine varieties. Izvestiya. Mathematics , Tome 6 (1972) no. 4, pp. 743-758. http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a3/

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