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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Rational surfaces with a~pencil of rational curves and with positive square of the canonical class},
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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/

[1] Yu. I. Manin, “Ratsionalnye $G$-poverkhnosti”, DAN SSSR, 175:1 (1967), 28–30 | MR | Zbl

[2] Yu. I. Manin, “Ratsionalnye poverkhnosti nad sovershennymi polyami. I”, Publ. Math. IHES, 30 (1966) | Zbl

[3] Yu. I. Manin, “Ratsionalnye poverkhnosti nad sovershennymi polyami. II”, Matem. sb., 72(114) (1967), 161–192 | MR | Zbl

[4] Yu. I. Manin, “Hypersurfaces cubiques. II”, Invent. Math., 6 (1969), 334–352 | DOI | MR | Zbl

[5] M. Nagata, “Ratsionalnye poverkhnosti. II”, Matematika, 8:4 (1964), 75–94

[6] V. A. Iskovskikh, “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh”, Matem. sb., 74(116) (1967), 608–638 | Zbl