Fronces et doubles plis

Jean-Pierre Henry; Michel Merle

Compositio Mathematica (1996)

  • Volume: 101, Issue: 1, page 21-54
  • ISSN: 0010-437X

How to cite


Henry, Jean-Pierre, and Merle, Michel. "Fronces et doubles plis." Compositio Mathematica 101.1 (1996): 21-54. <>.

author = {Henry, Jean-Pierre, Merle, Michel},
journal = {Compositio Mathematica},
keywords = {polar multiplicities; analytic invariants; polar variety; Zariski equisingularity},
language = {fre},
number = {1},
pages = {21-54},
publisher = {Kluwer Academic Publishers},
title = {Fronces et doubles plis},
url = {},
volume = {101},
year = {1996},

AU - Henry, Jean-Pierre
AU - Merle, Michel
TI - Fronces et doubles plis
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 101
IS - 1
SP - 21
EP - 54
LA - fre
KW - polar multiplicities; analytic invariants; polar variety; Zariski equisingularity
UR -
ER -


  1. 1 Briançon, J. and Henry, J.-P.: Équisingularité générique des familles de surfaces à singularité isolée. Bull. Soc. Math. Fr.1082 (1980) 259-281. Zbl0482.14004MR606093
  2. 2 Briançon, J. and Speder, J.-P.: Les conditions de Whitney impliquent μ* constant. Ann. Inst. Fourier26 (1976) 153-163. Zbl0331.32012
  3. 3 Fulton, W.: Intersection Theory. Ergebnisse der Mathematik3Folge. Band 2. Springer Verlag, 1984. Zbl0541.14005MR732620
  4. 4 Fulton, W., Kleiman, S.L. and McPherson, R.: About the enumeration of contacts. Algebraic Geometry, Proceedings Ravello (1982) 156-196. Zbl0529.14030MR714748
  5. 5 Henry, J.-P.: Numerical Invariants for Zariski Equisingularity. Proceedings of the workshop on resolution of singularities Università di Pisa, Dipartimento di Matematica, Sezione di Geometria e Algebra 1.82 (742) giugno1993. 
  6. 6 Henry, J.-P. and Lê, D.T.: Limites d'espaces tangents. Séminaire F. Norguet1974-75, Springer Lecture Notes482, pp. 251-265. Zbl0319.32019
  7. 7 Henry, J.-P. and Merle, M.: Limites d'espaces tangents et transversalité des variétés polaires. Actes de la conférence de la Rabida, Springer Lecture Notes961. Zbl0507.32005
  8. 8 Henry, J.-P. and Merle, M.: Limites de normales, conditions de Whitney et éclatement d'Hironaka. Proc. A.M.S. Summer Institute on Singularities, Arcata, 1981. Zbl0554.32010
  9. 9 Henry, J.-P. and Merle, M.: Conditions de régularité et éclatements. Ann. Inst. Fourier37, 3 (1987) 159-190. Zbl0596.32018MR916279
  10. 10 Henry, J.-P. and Merle, M.: Shade, Shadow and Shape. Chapitre "Geometry of Vision" pp. 143-168, in Artificial and Biological Vision Systems, G. A. Orban, H.-H. Nagel Editors, Esprit Series, edited in cooperation with the Commission of the European Communities, DG XIII, Springer Verlag1992. 
  11. 11 Henry, J.-P., Merle, M. and Sabbah, C.: Sur la condition de Thom stricte pour un morphisme analytique complexe. Ann. Scient. Ec. Norm. Sup.4ème série, 17, 1984. Zbl0551.32012MR760677
  12. 12 Hironaka, H.: Normal cones in Analytic Whitney Stratifications. Publ. Math.IH.B.S., 36, P.U.F., 1970. Zbl0219.57022MR277759
  13. 13 Hironaka, H.: Stratifications and Flatness in Real and Complex Singularities (Nordic Summer School, Oslo, 1976); Sijthoff and Noordhoff, 1977. Zbl0424.32004MR499286
  14. 14 Kashiwara, M.: B-functions and holonomic systems. Inv. Math.38 (1976), 33-53. Zbl0354.35082MR430304
  15. 15 Kashiwara, M.: Systèmes micro-différentiels. Cours à l'Université Paris-Nord. (Notes de T. Monteiro.) Progress in Maths. Birkhauser1983. 
  16. 16 Kashiwara, M. and Schapira, P.: Microlocal study of sheaves. Astérisque, 128, 1985. Zbl0589.32019MR794557
  17. 17 Kleiman, S.L.: On the Transversality of a General Translate. Compositio Math, 28 (1974) 287-297. Zbl0288.14014MR360616
  18. 18 Kleiman, S.L.: Tangency and Duality. Proc. 1984 Conf in algebraic geometry. CMS-AMS proceedings, 6 (1986) 163-226. Zbl0601.14046MR846021
  19. 19 Kleiman, S.L.: About the conormal scheme. Proc. Arcireale Conf. Lectures Notes1092, Springer. Zbl0547.14031MR775882
  20. 20 Kleiman, S.L.: Multiple-point Formulas for maps. Proc. Conf on Enumerative and classical Algebraic Geometry Progress in Maths. 24Birkhauser (1982) 237-252. Zbl0503.14023MR685771
  21. 21 Kleiman, S.L.: Multiple-point Formulas I: Iteration. Acta Math.147 (1981) 13-49. Zbl0479.14004MR631086
  22. 22 Lê, D.T. and Teissier, B.: Variétés polaires locales et classes de Chern des variétés singulières. Annals of Math., 114 (1981) 457-491. Zbl0488.32004MR634426
  23. 23 Lê, D.T. and Teissier, B.: Limites d'espaces tangents en géométrie analytique. Comment. Math. Helvetici, 63, 4 (1988) 540-578. Zbl0658.32010MR966949
  24. 24 Lipman, J.: Reduction, Blowing up and Multiplicities. Proc. Conf on Transcendental Methods in Commutative Algebra. George Mason University. Decker1979. 
  25. 25 Mather, J.: Stratifications and Mappings. in Dynamical Systems. M. Peixoto. (ed.) Academic Press. 1973. Zbl0286.58003MR368064
  26. 26 Pham, F. and Teissier, B.: Fractions lipschitziennes d'une algèbre analytique. Prépublication Centre de Maths. Ecole Polytechnique1969. 
  27. 27 Sabbah, C.: Quelques remarques sur la géométrie des espaces conormaux. Astérisque130 (1985) 161-192. Zbl0598.32011MR804052
  28. 28 Teissier, B.: Variétés polaires locales et conditions de Whitney. C. R. Acad. Sci. Paris. Série A-B290, 1980. Zbl0496.32009MR580569
  29. 29 Teissier, B.: Variétés polaires II. Actes de la conférence de la Rabida, Lectures Notes961, Springer. Zbl0585.14008
  30. 30 Thom, R.: Ensembles et morphismes stratifiés. Bull. Amer. Math. Soc., 75 (1969) 240-284. Zbl0197.20502MR239613
  31. 31 Verdier, J. -L.: Stratifications de Whitney et théorème de Bertini-Sard. Inv. Math., 36 (1976) 295-312. Zbl0333.32010MR481096
  32. 32 Whitney, H.: Tangents to an analytic variety. Ann. of Math.81 (1964) 496-549. Zbl0152.27701MR192520
  33. 33 Zariski, O.: Some open questions in the theory of singularities. Bull. A.M.S.77, 4 (1971) 481-491. Zbl0236.14002MR277533
  34. 34 Zariski, O.: Studies in equisingularity III. Amer. Jour. of Math.90 (1968) 961-1023. Zbl0189.21405MR237493
  35. 35 Zariski, O.: Foundations of a general theory of equisingularity on r-dimensional algebroid and algebraic varietes, of embedding dimension r+1. Amer. Jour. of Math.101 (1979) 453-514. Zbl0417.14008MR528001

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