Geodesic
Decomposition of certain birational morphisms
Izvestiya. Mathematics, Tome 16 (1981) no. 2, pp. 419-429 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that a projective birational morphism of smooth algebraic varieties whose fiber is no greater than one-dimensional can be factored into monoidal transformations with smooth centers of codimension 2. Bibliography: 6 titles. 
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     author = {V. I. Danilov},
     title = {Decomposition of certain birational morphisms},
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V. I. Danilov. Decomposition of certain birational morphisms. Izvestiya. Mathematics, Tome 16 (1981) no. 2, pp. 419-429. http://geodesic.mathdoc.fr/item/IM2_1981_16_2_a8/

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[3] Schafarewitsch I. R., Lectures on minimal models and birational transformations of two dimensional schemes, Bombay, 1966

[4] Manin Yu. I., “Lektsii o $K$-funktore v algebraicheskoi geometrii”, Uspekhi matem. nauk, 24:5 (1969), 3–86 | MR | Zbl

[5] Knutson D., Algebraic Spaces, Lect. Notes in Math., 203, 1971 | MR | Zbl

[6] Grothendiek A., Dieudonne J., Elements de géometrie algebrique, IV, Publ. Math. IHES, Paris, 1967