Journal of Algebraic Geometry

Author(s): Kalle Karu
Journal: J. Algebraic Geom. 14 (2005), 165-175.
Posted: August 31, 2004
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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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