Abstract
Affine surfaces X completed by an irreducible rational curve C are studied. The integer m = (C2) 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 Aut(X) is expressed by the stabilizers of the action. Explicit formulas for generators of the group Aut(X) are given for m ≤ 5. 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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