Geodesic
A filtration in the three-dimensional Cremona group
Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 191-208 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we introduce the concept of the genus of a birational mapping of nonsingular three-dimensional algebraic varieties over a field of characteristic 0 and prove that the automorphisms whose genus is at most a fixed number form a group. We also prove that a birational morphism of nonsingular three-dimensional varieties splits into a composition of a map which is an inverse to a morphism of genus 0 and monoidal transformations. Bibliography: 9 titles. 
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     author = {M. A. Frumkin},
     title = {A~filtration in the three-dimensional {Cremona} group},
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     url = {http://geodesic.mathdoc.fr/item/SM_1973_19_2_a3/}
}
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M. A. Frumkin. A filtration in the three-dimensional Cremona group. Sbornik. Mathematics, Tome 19 (1973) no. 2, pp. 191-208. http://geodesic.mathdoc.fr/item/SM_1973_19_2_a3/

[1] Algebraicheskie poverkhnosti, Trudy Matem. in-ta im. V. A. Steklova, LXXV, 1965 | MR | Zbl

[2] M. Baldassarri, Algebraicheskie mnogoobraziya, IL, Moskva, 1961 | MR

[3] P. Gabriel, M. Tsisman, Kategorii chastnykh i teoriya gomotopii, izd-vo «Mir», Moskva, 1971 | MR

[4] H. Hironaka, “An example of non-kählerian complex-analytic deformation of kählerian complex structures”, Ann. Math., 75:1 (1962), 190–208 | DOI | MR | Zbl

[5] Kh. Khironaka, “Razreshenie osobennostei algebraicheskikh mnogoobrazii nad polyami kharakteristiki 0”, Matematika, 9:6 (1965), 2–70; 10:1 (1966), 3–89 ; 10:2 (1966), 3–56 | MR | MR

[6] H. Hudson, Cremona transformations in plane and space, Univ. press., Cambrige, 1927 | Zbl

[7] V. A. Iskovskikh, Yu. I. Manin, “Trekhmernye kvartiki i kontrprimery k probleme Lyurota”, Matem. sb., 86 (128) (1971), 140–166 | MR | Zbl

[8] P. A. Clemens, C. H. Griffits, The intermediate jacobian of the cubic threefolds, preprint

[9] I. R. Shafarevich, “Lektsii po algebraicheskoi geometrii”, Uspekhi matem. nauk, XXIV:6 (150) (1969), 3–184 | MR