Geodesic
Rational $G$-surfaces
Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 103-134.

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In this paper the author determines the structure of complete rational surfaces on which one can define a group action in such a way that for each element of the group there exists a nonzero linear equivalence divisor class with nonnegative self-intersection index which is invariant with respect to this element. If one excludes the case when this action factors through an algebraic action of a linear algebraic group, then all such surfaces are elliptic bundles, and the action of the group preserves the family of fibers. Bibliography: 11 titles. 
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M. Kh. Gizatullin. Rational $G$-surfaces. Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 103-134. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a5/

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