Geodesic
Affine surfaces which are quasihomogeneous with respect to an algebraic group
Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 754-769

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In this paper we give a classification of affine surfaces which are quasihomogeneous with respect to an algebraic group. In particular, we also obtain a classification of affine surfaces which are homogeneous with respect to an algebraic group. 
@article{IM2_1971_5_4_a1,
     author = {M. Kh. Gizatullin},
     title = {Affine surfaces which are quasihomogeneous with respect to an algebraic group},
     journal = {Izvestiya. Mathematics },
     pages = {754--769},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a1/}
}
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M. Kh. Gizatullin. Affine surfaces which are quasihomogeneous with respect to an algebraic group. Izvestiya. Mathematics , Tome 5 (1971) no. 4, pp. 754-769. http://geodesic.mathdoc.fr/item/IM2_1971_5_4_a1/