Geodesic
Minimal models of rational surfaces over arbitrary fields
Izvestiya. Mathematics , Tome 14 (1980) no. 1, pp. 17-39

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In this article all the types of minimal models of smooth rational surfaces defined over an arbitrary field are described. Bibliography: 19 titles. 
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     title = {Minimal models of rational surfaces over arbitrary fields},
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V. A. Iskovskikh. Minimal models of rational surfaces over arbitrary fields. Izvestiya. Mathematics , Tome 14 (1980) no. 1, pp. 17-39. http://geodesic.mathdoc.fr/item/IM2_1980_14_1_a1/