Rational Surfaces With a Pencil of Rational Curves and With Positive Square of the Canonical Class

In the paper standard G-surfaces with a pencil of rational curves and with (?F ? ?F) > 0 are examined up to birational equivalence. It is proved that for (?F ? ?F) = 1 , 2 and 3 a birational class of these surfaces is uniquely determined by the birational class of their standard pencil of rational curves. For (?F ? ?F) > 4 each of these surfaces is birationally equivalent to either the plane P2 or some G-surface which is a biregular form of the surface P1?P1. Bibliography: 6 items.