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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Local strong factorization of toric birational maps

Author: Kalle Karu
Journal: J. Algebraic Geom. 14 (2005), 165-175
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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Kalle Karu
Affiliation: Department of Mathematics, Room 121, University of British Columbia, 1984 Mathematics Road, Vancouver, B.C. V6T 1Z2 Canada

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