Geodesic
Birational properties of a surface of degree 4 in $\mathbf P^4_k$
Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 30-36 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that a smooth surface of fourth degree in $\mathbf P^4_k$, defined over a perfect field $k$, is not birationally isomorphic, over $k$, to the projective plane $\mathbf P^2_k$ if it is $k$-minimal. Bibliography: 5 titles. 
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V. A. Iskovskikh. Birational properties of a surface of degree 4 in $\mathbf P^4_k$. Sbornik. Mathematics, Tome 17 (1972) no. 1, pp. 30-36. http://geodesic.mathdoc.fr/item/SM_1972_17_1_a1/

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

[2] V. A. Iskovskikh, “Ratsionalnye poverkhnosti s puchkom ratsionalnykh krivykh i s polozhitelnym kvadratom kanonicheskogo klassa”, Matem. sb., 83(125) (1970), 90–119 | Zbl

[3] Yu. I. Manin, Ratsionalnye poverkhnosti nad sovershennymi polyami. I, Publ. Math. IHES, 30, 1966 | Zbl

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

[5] M. Nagata, “Ratsionalnye poverkhnosti. I”, Matematika, 8:1 (1964), 55–81