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Uniform Linear Bound in Chevalley’s Lemma

Published online by Cambridge University Press:  20 November 2018

J. Adamus ,
E. Bierstone  and
P. D. Milman
J. Adamus
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, 00-956 Warszawa 10, Sniadeckich 8, Poland
E. Bierstone
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: [email protected], [email protected]
P. D. Milman
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: [email protected], [email protected]
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Abstract

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We obtain a uniform linear bound for the Chevalley function at a point in the source of an analytic mapping that is regular in the sense of Gabrielov. There is a version of Chevalley’s lemma also along a fibre, or at a point of the image of a proper analytic mapping. We get a uniform linear bound for the Chevalley function of a closed Nash (or formally Nash) subanalytic set.

Keywords

13J0732B2013J1032S10Keywords:Chevalley functionregular mappingNash subanalytic set
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 60 , Issue 4 , 01 August 2008 , pp. 721 - 733
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Bierstone, E. and Milman, P. D., Composite differentiable functions. Ann. of Math. 116(1982), no. 3, 541–558.Google Scholar
[2] Bierstone, E. and Milman, P. D., Relations among analytic functions. I. Ann. Inst. Fourier (Grenoble) 37(1987), no. 1, 187–239; Relations among analytic functions. II. 37(1987), no. 2, 49–77.Google Scholar
[3] Bierstone, E. and Milman, P. D., Geometric and differential properties of subanalytic sets. Ann. of Math. 147(1998), no. 3, 731–785.Google Scholar
[4] Chevalley, C., On the theory of local rings. Ann. of Math. 44(1943), 690–708.Google Scholar
[5] Duncan, A. J. and L. O’Carroll, A full uniform Artin-Rees theorem. J. Reine Agnew.Math. 394(1989), 203–207.Google Scholar
[6] Gabrielov, A. M., Formal relations between analytic functions. Math. USSR Izv. 7(1973), 1056–1088.Google Scholar
[7] Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. 79(1964), 109–326.Google Scholar
[8] Huneke, C., Uniform bounds in Noetherian rings. Invent.Math. 107(1992), no. 1, 203–223.Google Scholar
[9] Izumi, S., Linear complementary inequalities for orders of germs of analytic functions. Invent.Math. 65(1982), no. 3, 459–471.Google Scholar
[10] Izumi, S., Gabrielov's rank condition is equivalent to an inequality of reduced orders. Math. Ann. 276(1986), no. 1, 81–89.Google Scholar
[11] Paw, W.łucki, On Gabrielov's regularity condition for analytic mappings. Duke Math. J. 65(1992), no. 2, 299–311.Google Scholar
[12] Wang, T., Linear Chevalley estimates. Trans. Amer. Math. Soc. 347(1995), no. 12, 4877–4898.Google Scholar