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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     author = {\`E. B. Vinberg and V. L. Popov},
     title = {On a~class of quasihomogeneous affine varieties},
     journal = {Izvestiya. Mathematics },
     pages = {743--758},
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     volume = {6},
     number = {4},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_4_a3/}
}
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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/