On almost Blow-analytic equivalence

Details On almost Blow-analytic equivalence On almost Blow-analytic equivalence

2008-12-12

arxiv.org/abs/0812.2335v2

Proceedings of the London Mathematical Society 103, 4 (2011) 676-709

Mathematics

Algebraic Geometry

Proceedings of London Math. Soc., to appear

Scientific paper

Approximation of real analytic functions by Nash functions is a classical topic in real geometry. In this paper, we focus on the Nash approximation of an analytic desingularization of a Nash function germ obtained by a sequence of blowings-up along smooth analytic centers. We apply the result to prove that Nash function germs that are analytically equivalent after analytic desingularizations are Nash equivalent after Nash desingularizations. Results are based on a precise Euclidean description of a sequence of blowings-up combined with N\'eron Desingularization.

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