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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Torification and factorization of birational maps


Authors: Dan Abramovich, Kalle Karu, Kenji Matsuki and Jaroslaw Wlodarczyk
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
Email: abrmovic@math.bu.edu

Kalle Karu
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02139
Email: kkaru@math.harvard.edu

Kenji Matsuki
Affiliation: Department of Mathematics, Purdue University, 1395 Mathematical Sciences Building, West Lafayette, Indiana 47907-1395
Email: kmatsuki@math.purdue.edu

Jaroslaw Wlodarczyk
Affiliation: Instytut Matematyki UW, Banacha 2, 02-097 Warszawa, Poland
Email: jwlodar@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0894-0347-02-00396-X
PII: S 0894-0347(02)00396-X
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