Torification and factorization of birational maps

Abramovich, Dan; Karu, Kalle; Matsuki, Kenji; Włodarczyk, Jarosław

doi:10.1090/S0894-0347-02-00396-X

Torification and factorization of birational maps
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by Dan Abramovich, Kalle Karu, Kenji Matsuki and Jarosław Włodarczyk

J. Amer. Math. Soc. 15 (2002), 531-572

DOI: https://doi.org/10.1090/S0894-0347-02-00396-X

Published electronically: April 5, 2002

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Abstract:

Building on work of the fourth author and Morelli’s work, 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 nonsingular centers.

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