Stratification theory from the Newton polyhedron point of view
Annales de l'Institut Fourier, Volume 54 (2004) no. 2, p. 235-252
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.
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.
DOI : https://doi.org/10.5802/aif.2017
Classification:  14B05,  58A35,  14M25
Keywords: stratification, regularity condition, Newton polyhedron
@article{AIF_2004__54_2_235_0,
     author = {Abderrahmane, Ould M.},
     title = {Stratification theory from the Newton polyhedron point of view},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     pages = {235-252},
     doi = {10.5802/aif.2017},
     zbl = {1060.58005},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2004__54_2_235_0}
}
Stratification theory from the Newton polyhedron point of view. Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 235-252. doi : 10.5802/aif.2017. https://aif.centre-mersenne.org/item/AIF_2004__54_2_235_0/

[1] Ould. M. Abderrahmane Polyèdre de Newton et trivialité en famille, J. Math. Soc. Japan, Tome 54 (2002), pp. 513-550 | MR 1900955 | Zbl 1031.58024

[2] K. Bekka; D. Mond And J. Montaldi Eds (c)-régularité et trivialité topologique, Springer (SLNM) Tome 1462 (1989), pp. 42-62 | MR 1129023 | Zbl 0733.58003

[3] K. Bekka; S. Koike The Kuo condition, an inequality Thom's type and (c)-regularity, Topology, Tome 37 (1998), pp. 45-62 | MR 1480876 | Zbl 0894.58005

[4] J. Briançon; J.P. Speder La trivialité topologique n'implique pas les conditions de Whitney, C. R. Acad. Sci. Paris, Tome 280 (1976), pp. 365-367 | MR 425165 | Zbl 0331.32010

[5] J. Damon; T. Gaffney Topological Trivaility of Deformations of Functions and Newton filtrations, Invent. Math., Tome 72 (1983), pp. 335-358 | MR 704395 | Zbl 0519.58021

[6] T. Fukui; L. Paunescu Stratification theory from the weighted point of view, Canad. J. math, Tome 53 (2001), pp. 73-97 | MR 1814966 | Zbl 0983.32006

[7] A.G. Kouchnirenko Polyèdres de Newton et nombres de Milnor, Invent. math, Tome 32 (1976), pp. 1-31 | MR 419433 | Zbl 0328.32007

[8] T.-C. Kuo The ratio test for analytic Whitney stratification, Proc. of Liverpool Singularities, Springer (SLNM) Tome 192 (1971), pp. 141-149 | MR 279333 | Zbl 0246.32006

[9] M. Oka On the weak simultaneous resolution of a negligible truncation of the Newton boundary, Contemporary. Math, Tome 90 (1989), pp. 199-210 | MR 1000603 | Zbl 0682.32011

[10] L. Paunescu A weighted version of the Kuiper-Kuo-Bochnak-Łojasiewicz theorem, J. Algebraic Geom, Tome 2 (1993), pp. 69-79 | Zbl 0779.32003

[11] L. Paunescu Invariants associated with blow-analytic homeomorphisms, Proc. Japan Acad, ser. A, Tome 78 (2002), pp. 194-198 | MR 1950169 | Zbl 1040.32025

[12] A. Parusiński Topological triviality of μ-constant deformations of type f(x)+tg(x), Bull. London math. Soc, Tome 31 (1999), pp. 686-692 | MR 1711027 | Zbl 1020.32021

[13] R. Thom Ensembles et morphismes stratifiés, Bull. Amer. math. Soc, Tome 75 (1969), pp. 240-284 | MR 239613 | Zbl 0197.20502

[14] D. Trotman Comparing regularity conditions on stratification, Proc. Sympos. Pure. math, Tome 40 (1983), pp. 575-586 | MR 713282 | Zbl 0519.58009

[15] J.-L. Verdier Stratification de Whitney et théorème de Bertini-Sard, Invent. math, Tome 36 (1976), pp. 295-312 | MR 481096 | Zbl 0333.32010

[16] H. Whitney Tangents to an analytic variety, Ann. of Math, Tome 81 (1965), pp. 496-549 | MR 192520 | Zbl 0152.27701