Geodesic
Automorphisms of affine surfaces.~II
Izvestiya. Mathematics , Tome 11 (1977) no. 1, pp. 51-98.

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Affine surfaces $X$ completed by an irreducible rational curve $C$ are studied. The integer $m=(C^2)$ is an invariant of $X$. It is shown that the set of all such surfaces with fixed invariant $m$ is described in terms of orbits of a group action on the space of “tails”; moreover, the automorphism group $\operatorname{Aut}(X)$ is expressed by the stabilizers of the action. Explicit formulas for generators of the group $\operatorname{Aut}(X)$ are given for $m\leqslant5$. In particular, it is shown that in zero characteristic the invariant $m$ uniquely determines the surface $X$; in the general case this is not so. Bibliography: 11 titles. 
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M. Kh. Gizatullin; V. I. Danilov. Automorphisms of affine surfaces.~II. Izvestiya. Mathematics , Tome 11 (1977) no. 1, pp. 51-98. http://geodesic.mathdoc.fr/item/IM2_1977_11_1_a2/

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