Geodesic
Decomposition of certain birational morphisms
Izvestiya. Mathematics , Tome 16 (1981) no. 2, pp. 419-429

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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},
     journal = {Izvestiya. Mathematics },
     pages = {419--429},
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     number = {2},
     year = {1981},
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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/