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Torification and factorization of birational maps

Authors: Dan Abramovich, Kalle Karu, Kenji Matsuki and Jarosław Włodarczyk
Journal: J. Amer. Math. Soc. 15 (2002), 531-572
MSC (2000): Primary 14E05
Published electronically: April 5, 2002
MathSciNet review: 1896232
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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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Additional Information

Dan Abramovich
Affiliation: Department of Mathematics, Boston University, 111 Cummington Street, Boston, Massachusetts 02215
MR Author ID: 309312
ORCID: 0000-0003-0719-0989

Kalle Karu
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02139

Kenji Matsuki
Affiliation: Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395

Jarosław Włodarczyk
Affiliation: Instytut Matematyki UW, Banacha 2, 02-097 Warszawa, Poland

Received by editor(s): March 14, 2000
Received by editor(s) in revised form: June 1, 2000
Published electronically: April 5, 2002
Additional Notes: The first author was partially supported by NSF grant DMS-9700520 and by an Alfred P. Sloan research fellowship. In addition, he would like to thank the Institut des Hautes Études Scientifiques, Centre Emile Borel (UMS 839, CNRS/UPMC), and Max Planck Institut für Mathematik for a fruitful visiting period.
The second author was partially supported by NSF grant DMS-9700520
The third author has received no financial support from NSF or NSA during the course of this work.
The fourth author was supported in part by Polish KBN grant 2 P03 A 005 16 and NSF grant DMS-0100598.
Article copyright: © Copyright 2002 American Mathematical Society