Local monomialization of transcendental extensions
[Monomialisations locales des extensions transcendantes]
Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1517-1586.

Soient RS deux anneaux locaux réguliers, essentiellement de type fini sur un corps k de caractéristique zéro. Si V est un anneau de valuation du corps des fractions K de S dominant S, nous montrons qu’il existe des suites de transformés monoidaux (éclatements d’idéaux premiers réguliers) RR 1 et SS 1 le long de V tels que R 1 S 1 est une application monomiale. Il s’ensuit qu’un morphisme de variétés non singulières peut-être rendu monomial le long d’une valuation après éclatement de sous-variétés non singulières.

Suppose that RS are regular local rings which are essentially of finite type over a field k of characteristic zero. If V is a valuation ring of the quotient field K of S which dominates S, then we show that there are sequences of monoidal transforms (blow ups of regular primes) RR 1 and SS 1 along V such that R 1 S 1 is a monomial mapping. It follows that a morphism of nonsingular varieties can be made to be a monomial mapping along a valuation, after blow ups of nonsingular subvarieties.

DOI : 10.5802/aif.2132
Classification : 14E, 13A, 13B
Keywords: Monomialization, monoidal transform, valuation ring, Morphism
Mot clés : monomialisation, transformés monoidaux, anneaux de valuation, morphisme
Dale CUTKOSKY, Steven 1

1 University of Missouri, department of mathematics, Columbia, MO 65211 (USA)
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Dale CUTKOSKY, Steven. Local monomialization of transcendental extensions. Annales de l'Institut Fourier, Tome 55 (2005) no. 5, pp. 1517-1586. doi : 10.5802/aif.2132. http://www.numdam.org/articles/10.5802/aif.2132/

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