Stratification theory from the Newton polyhedron point of view

Ould M. Abderrahmane[1]

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

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 2, page 235-252
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Abderrahmane, Ould M.. "Stratification theory from the Newton polyhedron point of view." Annales de l’institut Fourier 54.2 (2004): 235-252. <http://eudml.org/doc/116110>.

@article{Abderrahmane2004,
abstract = {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.},
affiliation = {Saitama University, Faculty of Science, Department of Mathematics, 255 Shimo-Okubo, Urawa 338-8570 (Japon)},
author = {Abderrahmane, Ould M.},
journal = {Annales de l’institut Fourier},
keywords = {stratification; regularity condition; Newton polyhedron; singularities; stratified sets},
language = {eng},
number = {2},
pages = {235-252},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stratification theory from the Newton polyhedron point of view},
url = {http://eudml.org/doc/116110},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Abderrahmane, Ould M.
TI - Stratification theory from the Newton polyhedron point of view
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 2
SP - 235
EP - 252
AB - 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.
LA - eng
KW - stratification; regularity condition; Newton polyhedron; singularities; stratified sets
UR - http://eudml.org/doc/116110
ER -

References

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  1. Ould. M. Abderrahmane, Polyèdre de Newton et trivialité en famille, J. Math. Soc. Japan 54 (2002), 513-550 Zbl1031.58024MR1900955
  2. K. Bekka, ( c ) -régularité et trivialité topologique, 1462 (1989), 42-62, Springer Zbl0733.58003MR1129023
  3. K. Bekka, S. Koike, The Kuo condition, an inequality Thom’s type and ( c ) -regularity, Topology 37 (1998), 45-62 Zbl0894.58005MR1480876
  4. J. Briançon, J.P. Speder, La trivialité topologique n'implique pas les conditions de Whitney, C. R. Acad. Sci. Paris 280 (1976), 365-367 Zbl0331.32010MR425165
  5. J. Damon, T. Gaffney, Topological Trivaility of Deformations of Functions and Newton filtrations, Invent. Math. 72 (1983), 335-358 Zbl0519.58021MR704395
  6. T. Fukui, L. Paunescu, Stratification theory from the weighted point of view, Canad. J. math 53 (2001), 73-97 Zbl0983.32006MR1814966
  7. A.G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. math 32 (1976), 1-31 Zbl0328.32007MR419433
  8. T.-C. Kuo, The ratio test for analytic Whitney stratification, Proc. of Liverpool Singularities 192 (1971), 141-149, Springer Zbl0246.32006MR279333
  9. M. Oka, On the weak simultaneous resolution of a negligible truncation of the Newton boundary, Contemporary. Math 90 (1989), 199-210 Zbl0682.32011MR1000603
  10. L. Paunescu, A weighted version of the Kuiper-Kuo-Bochnak-Łojasiewicz theorem, J. Algebraic Geom 2 (1993), 69-79 Zbl0779.32003
  11. L. Paunescu, Invariants associated with blow-analytic homeomorphisms, Proc. Japan Acad, ser. A 78 (2002), 194-198 Zbl1040.32025MR1950169
  12. A. Parusiński, Topological triviality of μ -constant deformations of type f ( x ) + t g ( x ) , Bull. London math. Soc 31 (1999), 686-692 Zbl1020.32021MR1711027
  13. R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. math. Soc 75 (1969), 240-284 Zbl0197.20502MR239613
  14. D. Trotman, Comparing regularity conditions on stratification, Proc. Sympos. Pure. math 40 (1983), 575-586 Zbl0519.58009MR713282
  15. J.-L. Verdier, Stratification de Whitney et théorème de Bertini-Sard, Invent. math 36 (1976), 295-312 Zbl0333.32010MR481096
  16. H. Whitney, Tangents to an analytic variety, Ann. of Math 81 (1965), 496-549 Zbl0152.27701MR192520

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