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Torification and Factorization of Birational Maps

Dan Abramovich·Kalle Karu·Kenji Matsuki·Jarosław Włodarczyk
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Abstract

Building on the work of the fourth author in math.AG/9904074, we prove the weak factorization conjecture for birational maps in characteristic zero: a birational map between complete nonsingular varieties over an algebraically closed field K of characteristic zero is a composite of blowings up and blowings down with smooth centers. Such a factorization exists which is functorial with respect to absolute isomorphisms, and compatible with a normal crossings divisor. The same holds for algebraic and analytic spaces. Another proof of the main theorem by the fourth author appeared in math.AG/9904076.

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Dan Abramovich, Kalle Karu, Kenji Matsuki, Jarosław Włodarczyk. 2000-05-31. Torification and Factorization of Birational Maps. https://arxiv.org/abs/math/9904135

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