Geodesic
Rational surfaces with a~pencil of rational curves and with positive square of the canonical class
Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 91-117

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In the paper standard $G$-surfaces with a pencil of rational curves and with $(\omega_F\cdot\nobreak\omega_F)>\nobreak0$ are examined up to birational equivalence. It is proved that for $(\omega_F\cdot\omega_F)>1,2,3$ a birational class of these surfaces is uniquely determined by the birational class of their standard pencil of rational curves. For $(\omega_F\cdot\omega_F)>4$ each of these surfaces is birationally equivalent to either the plane $\mathbf P^2$ or some $G$-surface which is a biregular form of the surface $\mathbf P^1\times\mathbf P^1$. Bibliography: 6 titles. 
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     author = {V. A. Iskovskikh},
     title = {Rational surfaces with a~pencil of rational curves and with positive square of the canonical class},
     journal = {Sbornik. Mathematics},
     pages = {91--117},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1970_12_1_a5/}
}
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V. A. Iskovskikh. Rational surfaces with a~pencil of rational curves and with positive square of the canonical class. Sbornik. Mathematics, Tome 12 (1970) no. 1, pp. 91-117. http://geodesic.mathdoc.fr/item/SM_1970_12_1_a5/