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June 2011 $Q$-universal desingularization
Edward Bierstone, Pierre Milman, Michael Temkin
Asian J. Math. 15(2): 229-250 (June 2011).


We prove that the algorithm for desingularization of algebraic varieties in characteristic zero of the first two authors is functorial with respect to regular morphisms. For this purpose, we show that, in characteristic zero, a regular morphism with connected affine source can be factored into a smooth morphism, a ground-field extension and a generic-fibre embedding. Every variety of characteristic zero admits a regular morphism to a $Q$-variety. The desingularization algorithm is therefore $Q$-universal or absolute in the sense that it is induced from its restriction to varieties over $Q$. As a consequence, for example, the algorithm extends functorially to localizations and Henselizations of varieties.


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Edward Bierstone. Pierre Milman. Michael Temkin. "$Q$-universal desingularization." Asian J. Math. 15 (2) 229 - 250, June 2011.


Published: June 2011
First available in Project Euclid: 28 February 2012

zbMATH: 1267.14020
MathSciNet: MR2838221

Primary: 14E15 , 32S45
Secondary: 32S15 , 32S20

Keywords: canonical , functorial , marked ideal , resolution of singularities

Rights: Copyright © 2011 International Press of Boston


Vol.15 • No. 2 • June 2011
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