Équisingularité réelle : nombres de Lelong et images polaires

Georges Comte

Annales scientifiques de l'École Normale Supérieure (2000)

  • Volume: 33, Issue: 6, page 757-788
  • ISSN: 0012-9593

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Comte, Georges. "Équisingularité réelle : nombres de Lelong et images polaires." Annales scientifiques de l'École Normale Supérieure 33.6 (2000): 757-788. <http://eudml.org/doc/82533>.

@article{Comte2000,
author = {Comte, Georges},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Lelong numbers; polar varieties; equisingularity},
language = {fre},
number = {6},
pages = {757-788},
publisher = {Elsevier},
title = {Équisingularité réelle : nombres de Lelong et images polaires},
url = {http://eudml.org/doc/82533},
volume = {33},
year = {2000},
}

TY - JOUR
AU - Comte, Georges
TI - Équisingularité réelle : nombres de Lelong et images polaires
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2000
PB - Elsevier
VL - 33
IS - 6
SP - 757
EP - 788
LA - fre
KW - Lelong numbers; polar varieties; equisingularity
UR - http://eudml.org/doc/82533
ER -

References

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  1. [1] BESICOVITCH A.S., On the fundamental geometric properties of linearly measurable plane sets of points (I), (II), (III), Math. Ann. 98, 115, 116 (1927, 1938, 1939) 422-464, 296-329, 346-357. Zbl53.0175.04JFM53.0175.04
  2. [2] BRIANÇON J., SPEDER J.P., Les conditions de Whitney impliquent µ* constant, Ann. Inst. Fourier, Grenoble 26 (1976) 153-163. Zbl0331.32012MR54 #7843
  3. [3] BRODERSEN H., TROTMAN D., Whitney (b)-regularity is strictly weaker than Kuo's ratio test for real algebraic stratifications, Math. Scand. 45 (1979) 27-34. Zbl0429.58001MR81i:58008
  4. [4] COMTE G., Multiplicity of complex analytic sets and bilipschitz maps, in : Fukuda T., Fukui T., Izumiya S., Koike S. (Eds.), Real Analytic and Algebraic Singularities, Pitman Research Notes in Mathematics Series, Vol. 381, 1998, pp. 182-188. Zbl0982.32026MR99a:32048
  5. [5] COMTE G., Formule de Cauchy-Crofton pour la densité des ensembles sous-analytiques, C. R. Acad. Sci. Paris, Série I 328 (1999) 505-508. Zbl0945.32019MR2000b:32015
  6. [6] COMTE G., LION J.-M., ROLIN J.-P., Nature Log-analytique du volume des sous-analytiques, Illinois J. Math. (à paraître). Zbl0982.32009
  7. [7] DEMAILLY J.-P., Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité, Acta Math. 159 (3-4) (1987) 153-169. Zbl0629.32011MR89b:32019
  8. [8] DENKOWSKA Z., ŁOJASIEWICZ S., STASICA J., Sur le nombre de composantes connexes de la section d'un sous-analytique, Bull. Acad. Pol. Sci. XXX (7-8) (1982) 333-335. Zbl0527.32007
  9. [9] DENKOWSKA Z., STASICA J., Ensembles sous-analytiques à la polonaise, 1985. Zbl0584.32013
  10. [10] DENKOWSKA Z., WACHTA K., Sur la sous-analyticité de l'application tangente, Bull. Acad. Pol. Sci. XXX (7-8) (1982) 329-331. Zbl0526.32007
  11. [11] DRAPER R.N., Intersection theory in analytic geometry, Math. Ann. 180 (1969) 175-204. Zbl0157.40502MR40 #403
  12. [12] VAN DEN DRIES L., MILLER C., Geometric categories and o-minimal structures, Duke Math. J. 84 (1996) 497-540. Zbl0889.03025MR97i:32008
  13. [13] FEDERER H., The (Φ, k) rectifiable subsets of n-space, Trans. Amer. Math. Soc. 62 (1947) 114-192. Zbl0032.14902MR9,231c
  14. [14] FEDERER H., Geometric Measure Theory, Grundlehren Math. Wiss., Vol. 153, Springer-Verlag, 1969. Zbl0176.00801MR41 #1976
  15. [15] GABRIELOV A.M., Projections of semianalytic sets, Funkcional. Anal. i Priložen. 2 (4) (1968) 418-430. Zbl0179.08503MR39 #7137
  16. [16] GORESKY M., MACPHERSON R., Stratified Morse Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), Vol. 14, Springer-Verlag, 1988. Zbl0639.14012MR90d:57039
  17. [17] HARDT R.M., Topological properties of subanalytic sets, Trans. Amer. Math. Soc. 211 (1975) 57-70. Zbl0303.32008MR52 #787
  18. [18] HARDT R.M., Stratifications of real analytic mappings and images, Invent. Math. 28 (1975) 193-208. Zbl0298.32003MR51 #8453
  19. [19] HARDT R.M., Semialgebraic local triviality in semialgebraic mappings, Amer. J. Math. 102 (1980) 291-302. Zbl0465.14012MR81d:32012
  20. [20] HENRY J.-P., MERLE M., Stratifications de Whitney d'un ensemble sous-analytique, C. R. Acad. Sci. Paris, Série A 308 (1989) 357-360. Zbl0671.32013MR90d:32015
  21. [21] HENRY J.-P., MERLE M., Limites de normales, conditions de Whitney et éclatement d'Hironaka, in : Proc. Symp. in Pure Math. 40, Vol. 1, Arcata 1981, Amer. Math. Soc., 1983, pp. 575-584. Zbl0554.32010MR85i:32018
  22. [22] HENRY J.-P., MERLE M., Conditions de régularité et éclatements, Ann. Inst. Fourier, Grenoble 37 (1987) 159-190. Zbl0596.32018MR89d:32015
  23. [23] HENRY J.-P., MERLE M., SABBAH C., Sur la condition de Thom stricte pour un morphisme analytique complexe, Ann. Scient. Éc. Norm. Sup. 17 (1984) 227-268. Zbl0551.32012MR86m:32019
  24. [24] HIRONAKA H., Normal cones in analytic Whitney stratifications, Publ. Math. Inst. Hautes Études Sci. 36 (1970) 127-138. Zbl0219.57022MR43 #3492
  25. [25] HIRONAKA H., Subanalytic sets, in : Number Theory, Algebraic Geometry and Commutative Algebra, Kinokuniya, Tokyo, 1973, pp. 453-493. Zbl0297.32008MR51 #13275
  26. [26] KLEIMAN S., On the transversality of a general translate, Compositio Math. 28 (1974) 287-297. Zbl0288.14014MR50 #13063
  27. [27] KUO T.C., The ratio test for analytic Whitney stratifications, in : Wall C.T.C. (Ed.), Liverpool Singularities Symposium I, Lect. Notes in Math., Vol. 192, 1971, pp. 141-149. Zbl0246.32006MR43 #5056
  28. [28] KURDYKA K., Points réguliers d'un sous-analytique, Ann. Inst. Fourier, Grenoble 38 (1988) 133-156. Zbl0619.32007MR89g:32010
  29. [29] KURDYKA K., RABY G., Densité des ensembles sous-analytiques, Ann. Inst. Fourier, Grenoble 39 (1989) 753-771. Zbl0673.32015MR90k:32026
  30. [30] LELONG P., Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957) 239-262. Zbl0079.30901MR20 #2465
  31. [31] LÊ DŨNG TRÁNG, RAMANUJAM C.P., The invariance of Milnor's number implies the invariance of the topological type, Amer. J. of Math. 98 (1976) 67-78. Zbl0351.32009MR53 #2939
  32. [32] LÊ DŨNG TRÁNG, TEISSIER B., Variétés polaires locales et classes de Chern des variétés singulières, Ann. Math. 114 (1981) 457-491. Zbl0488.32004MR83k:32012a
  33. [33] LÊ DŨNG TRÁNG, TEISSIER B., Cycles évanescents et conditions de Whitney II, in : Proc. Symp. in Pure Math. 40, Vol. 2, Arcata 1981, Amer. Math. Soc., 1983, pp. 65-103. Zbl0532.32003MR86c:32005
  34. [34] LION J.-M., ROLIN J.-P., Théorème de préparation pour les fonctions logarithmico-exponentielles, Ann. Inst. Fourier, Grenoble 47 (1997) 859-884. Zbl0873.32004MR98h:32009
  35. [35] LION J.-M., ROLIN J.-P., Intégration des fonctions sous-analytiques et volume des sous-ensembles sous-analytiques, Ann. Inst. Fourier, Grenoble 48 (1998) 755-767. Zbl0912.32007MR2000i:32011
  36. [36] LIPMAN J.H., Equimultiplicity, reduction and blowing-up, in : Proc. Conference on Transcendental Methods in Commutative Algebra (1979), Lect. Notes in P. and Appl. Math., Vol. 68, Dekker, New York, 1982, pp. 111-147. Zbl0508.13013MR84a:13023
  37. [37] MATHER J., Notes on Topological Stability, Harvard University, 1970. 
  38. [38] MAWOUSSI K.Y., Conditions de Whitney et variétés polaires en géométrie analytique réelle, Thèse, Université Paris-7, Denis-Diderot, 1997. 
  39. [39] NAVARRO AZNAR V., Conditions de Whitney et sections planes, Invent. Math. 61 (1980) 199-226. Zbl0449.32013MR82h:32019
  40. [40] NAVARRO AZNAR V., TROTMAN D., Whitney regularity and generic wings, Ann. Inst. Fourier, Grenoble 31 (1981) 87-111. Zbl0442.58002MR82j:58009
  41. [41] ORRO P., Conditions de régularité, espaces tangents et fonctions de Morse, Thèse, Orsay, 1984. 
  42. [42] ORRO P., TROTMAN D., On the regular stratifications and conormal structure of subanalytic sets, Bull. London Math. Soc. 18 (1986) 185-191. Zbl0585.32006MR88d:32023
  43. [43] ORRO P., TROTMAN D., Cône normal et régularités de Kuo-Verdier, Preprint. Zbl1014.58004
  44. [44] PARUSIŃSKI A., Lipschitz stratifications of subanalytic sets, Ann. Scient. Éc. Norm. Sup. 4e série 27 (1994) 661-696. Zbl0819.32007MR96g:32017
  45. [45] PAWŁUCKI W., Quasi-regular boundary and Stokes formula for a subanalytic leaf, in : Seminar on Deformations, Łodz-Warsaw (1981-1983), Lect. Notes in Math., Vol. 1165, Springer-Verlag, 1985, pp. 235-252. Zbl0594.32011
  46. [46] SANTALÓ L.A., Integral geometry and geometric probability, in : Encyclopedia of Mathematics and its Applications, Vol. 1, Addison-Wesley, Reading, MA, 1976. Zbl0342.53049MR55 #6340
  47. [47] SCHICKHOFF W., Whitneysche Tangentenkegel, Multiplizitätsverhalten, Normal-Pseudoflachheit und Äquisingularitätstheorie für Ramissche Räume, Schriftenreihe des Math. Inst. des Universität Münster 2, Serie Heft 12 (1977). Zbl0379.32024
  48. [48] SIERPIŃSKI W., Sur la densité des ensembles plans, Fund. Math. 9 (1927) 172-185. JFM53.0176.01
  49. [49] SIU Y.T., Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27 (1974) 53-156. Zbl0289.32003MR50 #5003
  50. [50] SPEDER J.P., Équisingularité et conditions de Whitney, Amer. J. of Math. 97 (3) (1974) 571-588. Zbl0323.14006MR56 #3015
  51. [51] STOLL W., Mehrfache Integrale auf komplexen Mannigfaltigkeiten, Math. Z. 57 (1952) 116-154. Zbl0047.32401MR14,550e
  52. [52] TAMM M., Subanalytic sets in the calculus of variations, Acta Math. 146 (1981) 167-199. Zbl0478.58010MR82h:32012
  53. [53] TEISSIER B., Cycles évanescents, sections planes et conditions de Whitney, in : Singularités à Cargèse, Astérisque, Vol. 7-8, 1973, pp. 285-362. Zbl0295.14003MR51 #10682
  54. [54] TEISSIER B., Introduction to equisingularity problems, in : Proc. Symp. in Pure Math. 29, Arcata 1974, Amer. Math. Soc., 1975, pp. 593-632. Zbl0322.14008MR54 #10247
  55. [55] TEISSIER B., Variétés polaires II : multiplicités polaires, sections planes et conditions de Whitney, in : Actes de la conférence de géométrie algébrique à la Ràbida, Lect. Notes in Math., Vol. 961, Springer-Verlag, 1981, pp. 314-491. Zbl0585.14008MR85i:32019
  56. [56] TEISSIER B., Tame and stratified objects, in : Geometric Galois Actions, 1. Around Grothendieck's esquisse d'un Programme, London Math. Soc. Lecture Note Series, Vol. 242, 1997, pp. 231-242. Zbl0920.18002MR98k:14080
  57. [57] THIE P., The Lelong number of a point of a complex analytic set, Math. Ann. 172 (1967) 269-312. Zbl0158.32804MR35 #5661
  58. [58] THOM R., Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969) 240-284. Zbl0197.20502MR39 #970
  59. [59] TROTMAN D., Comparing regularity conditions on stratifications, in : Proc. Symp. in Pure Math. 40, Vol. 2, Arcata 1981, Amer. Math. Soc., 1983, pp. 575-586. Zbl0519.58009MR84j:58021
  60. [60] A.N. VARCHENKO, Theorems of topological equisingularity, Izvestia Ak. Nauk SSSR, Ser. Math. 36 (1972). 
  61. [61] VARCHENKO A.N., Algebro-geometrical equisingularity and local topological classification of smooth mappings, in : Proc. Int. Congress of Mathematicians, Vol. 1, Vancouver B.C., 1974, Canad. Math. Congress, Montreal, Quebec, 1975, pp. 427-431. Zbl0333.14005MR54 #12763
  62. [62] VERDIER J.-L., Stratifications de Whitney et théorème de Bertini-Sard, Invent. Math. 36 (1976) 295-312. Zbl0333.32010MR58 #1242
  63. [63] WHITNEY H., Complex Analytic Varieties, Addison-Wesley, Reading, MA, 1972. Zbl0265.32008MR52 #8473
  64. [64] ZARISKI O., Studies in equisingularity (I), (II), (III), Amer. J. of Math. 87, 87, 90 (1965, 1965, 1968) 507-536, 972-1006, 961-1023. Zbl0189.21405MR31 #2243
  65. [65] ZARISKI O., Some open questions in the theory of singularities, Bull. Amer. Math. Soc. 77 (1971) 481-491. Zbl0236.14002MR43 #3266
  66. [66] ZARISKI O., On equimultiple subvarieties of algebroid hypersurfaces, Proc. Nat. Acad. Sci. USA 72 (4) (1975) 1425-1426 [Correction : Proc. Nat. Acad. Sci. USA 72 (8) (1975) 3260]. Zbl0304.14008MR52 #10724a
  67. [67] ZARISKI O., Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varieties, of embedding dimension r + 1, Amer. J. of Math. 101 (1979) 453-514. Zbl0417.14008MR81m:14005

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