Local strong factorization of toric birational maps
Author:
Kalle Karu
Journal:
J. Algebraic Geom. 14 (2005), 165-175
DOI:
https://doi.org/10.1090/S1056-3911-04-00380-7
Published electronically:
August 31, 2004
MathSciNet review:
2092130
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Abstract |
References |
Additional Information
Abstract: The strong factorization conjecture states that a proper birational map between smooth algebraic varieties over a field of characteristic zero can be factored as a sequence of smooth blowups followed by a sequence of smooth blowdowns. We prove a local version of the strong factorization conjecture for toric varieties. Combining this result with the monomialization theorem of S. D. Cutkosky, we obtain a strong factorization theorem for local rings dominated by a valuation.
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- Dan Abramovich, Kenji Matsuki, and Suliman Rashid, A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension, Tohoku Math. J. (2) 51 (1999), no. 4, 489–537. MR 1725624, DOI https://doi.org/10.2748/tmj/1178224717
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AbramovichMatsukiRashid D. Abramovich, K. Matsuki and S. Rashid, A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension, Tohoku Math. J. (2) 51 (1999), no. 4, 489-537.
Christensen C. Christensen, Strong domination/weak factorization of three dimensional regular local rings, Journal of the Indian Math. Soc. 45, 1981, p. 21-47.
Cutkosky1 S. D. Cutkosky, Local factorization of birational maps, Advances in math. 132, 1997, p. 167-315.
Cutkosky2 S. D. Cutkosky, Local monomialization and factorization of morphisms, Astérisque No. 260 (1999), p. vi-143.
Matsuki K. Matsuki, Correction: “A note on the factorization theorem of toric birational maps after Morelli and its toroidal extension" [Tohoku Math. J. (2) 51 (1999), no. 4, 489–537] by D. Abramovich, K. Matsuki and S. Rashid, Tohoku Math. J. (2) 52 (2000), no. 4, 629–631.
Morelli1 R. Morelli, The birational geometry of toric varieties, J. Alg. Geom. 5 1996, 751-782.
Wlodarczyk3 J. Włodarczyk, Decomposition of birational toric maps in blow-ups and blow-downs, Trans. Amer. Math. Soc. 349 (1997), no. 1, 373-411.
Additional Information
Kalle Karu
Affiliation:
Department of Mathematics, Room 121, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C. V6T 1Z2 Canada
Email:
karu@math.ubc.ca
Received by editor(s):
May 22, 2003
Received by editor(s) in revised form:
December 5, 2003
Published electronically:
August 31, 2004
Additional Notes:
The author was partially supported by NSF grant DMS-0070678
