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
DOI:
https://doi.org/10.1090/S0894-0347-02-00396-X
Published electronically:
April 5, 2002
MathSciNet review:
1896232
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Abstract | References | Similar Articles | Additional Information
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 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:
https://doi.org/10.1090/S0894-0347-02-00396-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.
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American Mathematical Society