Stratification theory from the Newton polyhedron point of view

Abderrahmane, Ould M.

doi:10.5802/aif.2017

Stratification theory from the Newton polyhedron point of view
[La théorie de la stratification relatif à un polyèdre de Newton]

Abderrahmane, Ould M.¹

¹ Saitama University, Faculty of Science, Department of Mathematics, 255 Shimo-Okubo, Urawa 338-8570 (Japon)

Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 235-252.

Résumé
Abstract

Récement, T. Fukui et L. Paunescu ont introduit une version relative avec poids de la condition $(w)$ -régularité. Dans cette approche nous considérons les conditions $(w)$ - régularité et $(c)$ -régularité liées à une filtration de Newton.

Recently, T. Fukui and L. Paunescu introduced a weighted version of the $(w)$ -regularity condition and Kuo’s ratio test condition. In this approach, we consider the $(w)$ - regularity condition and $(c)$ -regularity related to a Newton filtration.

Zbl

DOI : 10.5802/aif.2017

Classification : 14B05, 58A35, 14M25
Keywords: stratification, regularity condition, Newton polyhedron
Mot clés : stratification, condition de régularité, polyèdre de Newton

Affiliations des auteurs :

Abderrahmane, Ould M. ¹

¹ Saitama University, Faculty of Science, Department of Mathematics, 255 Shimo-Okubo, Urawa 338-8570 (Japon)

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     title = {Stratification theory from the {Newton} polyhedron point of view},
     journal = {Annales de l'Institut Fourier},
     pages = {235--252},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     doi = {10.5802/aif.2017},
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Abderrahmane, Ould M. Stratification theory from the Newton polyhedron point of view. Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 235-252. doi : 10.5802/aif.2017. http://archive.numdam.org/articles/10.5802/aif.2017/

Bibliographie
Cité par

[1] Ould. M. Abderrahmane Polyèdre de Newton et trivialité en famille, J. Math. Soc. Japan, Volume 54 (2002), pp. 513-550 | MR | Zbl

[2] K. Bekka; D. Mond and J. Montaldi Eds $(c)$ -régularité et trivialité topologique (SLNM), Volume 1462 (1989), pp. 42-62 | MR | Zbl

[3] K. Bekka; S. Koike The Kuo condition, an inequality Thom's type and $(c)$ -regularity, Topology, Volume 37 (1998), pp. 45-62 | MR | Zbl

[4] J. Briançon; J.P. Speder La trivialité topologique n'implique pas les conditions de Whitney, C. R. Acad. Sci. Paris, Volume 280 (1976), pp. 365-367 | MR | Zbl

[5] J. Damon; T. Gaffney Topological Trivaility of Deformations of Functions and Newton filtrations, Invent. Math., Volume 72 (1983), pp. 335-358 | MR | Zbl

[6] T. Fukui; L. Paunescu Stratification theory from the weighted point of view, Canad. J. math, Volume 53 (2001), pp. 73-97 | MR | Zbl

[7] A.G. Kouchnirenko Polyèdres de Newton et nombres de Milnor, Invent. math, Volume 32 (1976), pp. 1-31 | MR | Zbl

[8] T.-C. Kuo The ratio test for analytic Whitney stratification, Proc. of Liverpool Singularities (SLNM), Volume 192 (1971), pp. 141-149 | MR | Zbl

[9] M. Oka On the weak simultaneous resolution of a negligible truncation of the Newton boundary, Contemporary. Math, Volume 90 (1989), pp. 199-210 | MR | Zbl

[10] L. Paunescu A weighted version of the Kuiper-Kuo-Bochnak-Łojasiewicz theorem, J. Algebraic Geom, Volume 2 (1993), pp. 69-79 | Zbl

[11] L. Paunescu Invariants associated with blow-analytic homeomorphisms, Proc. Japan Acad, ser. A, Volume 78 (2002), pp. 194-198 | MR | Zbl

[12] A. Parusiński Topological triviality of $μ$ -constant deformations of type $f (x) + t g (x)$ , Bull. London math. Soc, Volume 31 (1999), pp. 686-692 | MR | Zbl

[13] R. Thom Ensembles et morphismes stratifiés, Bull. Amer. math. Soc, Volume 75 (1969), pp. 240-284 | MR | Zbl

[14] D. Trotman Comparing regularity conditions on stratification, Proc. Sympos. Pure. math, Volume 40 (1983), pp. 575-586 | MR | Zbl

[15] J.-L. Verdier Stratification de Whitney et théorème de Bertini-Sard, Invent. math, Volume 36 (1976), pp. 295-312 | MR | Zbl

[16] H. Whitney Tangents to an analytic variety, Ann. of Math, Volume 81 (1965), pp. 496-549 | MR | Zbl

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