Illinois Journal of Mathematics

Factorizations of birational extensions of local rings

Steven Dale Cutkosky and Hema Srinivasan

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735323

Digital Object Identifier
doi:10.1215/ijm/1258735323

Mathematical Reviews number (MathSciNet)
MR2346185

Zentralblatt MATH identifier
1132.14013

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

Citation

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. https://projecteuclid.org/euclid.ijm/1258735323


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