Rational $G$-surfaces

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.