Geodesic
Decomposition of a birational map of three-dimensional varieties outside codimension 2
Izvestiya. Mathematics, Tome 21 (1983) no. 1, pp. 187-200 
Vik. S. Kulikov. Decomposition of a birational map of three-dimensional varieties outside codimension 2. Izvestiya. Mathematics, Tome 21 (1983) no. 1, pp. 187-200. http://geodesic.mathdoc.fr/item/IM2_1983_21_1_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The main result is the proof of the fact that one can perform a finite number of monoidal transformations with nonsingular centers in such a way that any two nonsingular birationally isomorphic threefolds become isomorphic outside codimension $2$, and the subsets at which the varieties are not isomorphic consist of unions of nonsingular rational curves transversally intersecting with each other. Bibliography: 8 titles.

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[2] Crauder B., Birational morphisms of smooth algebraic 3-folds collapsing three surfaces to a point, preprint, 1980

[3] Crauder B., Birational morphisms of smooth algebraic 3-folds collapsing a divisor with no triple points to a point, preprint, 1980

[4] Schaps M., “Birational morphisms factorizable by two monoidal transformations”, Math. Annal., 222 (1976), 23–28 | DOI | MR | Zbl

[5] Kulikov V. S., “Vyrozhdeniya $K3$ poverkhnostei”, Izv. AN SSSR. Ser. matem., 41:5 (1977), 1008–1042 | MR | Zbl

[6] Nakano S., “On the inverse of monoidal transformations”, Publ. Res. Inst. Math. Sci., 6 (1970/71), 483–502 | DOI | MR

[7] Hironaka H., “Resolutions of singularities over fields of characteristic zero. I”, Ann. of Math. (2), 79 (1964), 109–203 | DOI | MR | Zbl

[8] Shafarovich I. R., Osnovy algebraicheskoi geometrii, Nauka, M., 1972 | MR