Illinois Journal of Mathematics

Factorizations of birational extensions of local rings

Steven Dale Cutkosky and Hema Srinivasan

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We give a proof of local strong factorization of a birational, monomial extension of regular local rings along a valuation of rank 1 and maximal rational rank. Our proof uses methods from linear algebra, and is in the spirit of Christensen's proof of this result in dimension 3. This has also been proven by Karu using toric geometry.

Article information

Illinois J. Math., Volume 51, Number 1 (2007), 41-56.

First available in Project Euclid: 20 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13B10: Morphisms
Secondary: 13A18: Valuations and their generalizations [See also 12J20] 13F30: Valuation rings [See also 13A18] 14E05: Rational and birational maps


Cutkosky, Steven Dale; Srinivasan, Hema. Factorizations of birational extensions of local rings. Illinois J. Math. 51 (2007), no. 1, 41--56. doi:10.1215/ijm/1258735323.

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