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Theorems of factorizations for birational morphisms. (English) Zbl 0687.14009
Theorems on the factorization of birational morphisms between regular schemes by blowing ups are proved. The main theorem is that every projective and birational morphism between regular schemes, the fibres of which are of dimension $$\leq 1$$, is a composition of blowing ups at regular centres. This theorem generalizes the Danilov theorem [V. I. Danilov, Math. USSR, Izv. 16, 419-429 (1981); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 44, 465-477 (1980; Zbl 0453.14004)] from the case of smooth algebraic varieties to that of regular schemes.
Reviewer: T.Krasiński

##### MSC:
 1.4e+06 Rational and birational maps
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##### References:
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