Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique

Michel Hickel

Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)

  • Volume: 14, Issue: 1, page 1-50
  • ISSN: 0240-2963

How to cite

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Hickel, Michel. "Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.1 (2005): 1-50. <http://eudml.org/doc/73643>.

@article{Hickel2005,
author = {Hickel, Michel},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {germ of real or complex analytic space; space of germs of arcs; Nash sequence of multiplicities along an arc; Nash sequence of Hilbert-Samuel functions; Nash sequence of diagram of initial exponents; Lojasiewicz bundle inequalities at the level of arcs; principal strata; motivic volume; motivic integration; rank condition of Gabrielov},
language = {fre},
number = {1},
pages = {1-50},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique},
url = {http://eudml.org/doc/73643},
volume = {14},
year = {2005},
}

TY - JOUR
AU - Hickel, Michel
TI - Sur quelques aspects de la géométrie de l'espace des arcs tracés sur un espace analytique
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2005
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 1
SP - 1
EP - 50
LA - fre
KW - germ of real or complex analytic space; space of germs of arcs; Nash sequence of multiplicities along an arc; Nash sequence of Hilbert-Samuel functions; Nash sequence of diagram of initial exponents; Lojasiewicz bundle inequalities at the level of arcs; principal strata; motivic volume; motivic integration; rank condition of Gabrielov
UR - http://eudml.org/doc/73643
ER -

References

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  1. [A1] Artin ( M. ), Algebraic approximation of structures over complete local rings, Pub. Math. I.H.E.S.36, p. 23-58 (1969). Zbl0181.48802MR268188
  2. [B] Bennett ( B.M. ), On the characteristic function of a local ring, Ann. of Math. (2) 91, p. 25-87 (1970). Zbl0198.06101MR252388
  3. [B-M1] Bierstone ( E.), Milman ( P.D.), Relations among analytic functions I, Ann. Inst. Fourier (Grenoble), (1) 37, p. 187-239 (1987). Zbl0611.32002MR894566
  4. [B-M2] Bierstone ( E.), Milman ( P.D.), Uniformization of analytic spaces, Jour. A.M.S.2, p. 801-836 (1989). Zbl0685.32007MR1001853
  5. [B-M3] Bierstone ( E. ), Milman ( P.D.), Geometric and differential properties of subanalytic sets, Ann. of Math.147, p. 731-785 (1998). Zbl0912.32006MR1637671
  6. [D-L1] Denef ( J.) , Loeser ( F.), Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math.135, p. 201-232 (1999). Zbl0928.14004MR1664700
  7. [D-L2] Denef ( J.), Loeser ( F.), Geometry on arc spaces of algebraic varieties, in European Congress of Mathematics, vol I (Barcelona, 2000), Prog. Math., vol. 201, Birkhäuser , p. 327-348 (2001). Zbl1079.14003MR1905328
  8. [Ga] Gabrielov ( A.M.), Formal relations between analytic functions , Izv. Akad. Nauk. SSSR.37, p. 1056-1088 (1973). Zbl0297.32007MR346184
  9. [Gr] Greenberg ( M.), Rational points in henselian discrete valuation rings, Pub. Math. I.H.E.S.31, p. 59-64 (1966). Zbl0146.42201MR207700
  10. [G-S-L-J] Gonzalez-Sprinberg ( G.), Lejeune-Jalabert ( M.), Sur l'espace des courbes tracées sur une singularité, Prog. Math.134, p. 8-32 (1996). Zbl0862.14003
  11. [H1] Hickel ( M. ), Fonction de Artin et germes de courbes tracées sur un germe d'espace analytique, Amer. J. Math.115, p. 1299-1334 (1993). Zbl0804.32006MR1254735
  12. [H2] Hickel ( M. ), Calcul de la fonction d'Artin-Greenberg d'une branche plane, Pacific Journal of math.213, p.37-47 (2004), et Preprint Université Bordeaux I N°145 (Avril 2002 ). Zbl1054.14036
  13. [I-K] Ishii ( S. ) and Kollár ( J.), The Nash problem on arc families of singularities, Duke Math. J.120, p. 601-620 (2003). Zbl1052.14011MR2030097
  14. [I1] Izumi ( S. ), Linear complementary inequalities for orders of germs of analytic functions, Invent. Math.65, p. 459-471 (1982). Zbl0497.32005MR643564
  15. [12] Izumi ( S. ), A measure of integrity for local analytic algebras, Pub. R.I.M.S, Kyoto Univ.21, p. 719-735 (1985). Zbl0587.32016MR817161
  16. [13] Izumi ( S. ), Gabrielov's Rang Condition is equivalent to an inequality of reduced orders, Math. Ann.276, p. 81-89 (1986). Zbl0612.32013MR863708
  17. [14] Izumi ( S. ), The rank condition and convergence of formal functions, Duke Math. J.59, p. 241-264 (1989). Zbl0688.32008MR1016886
  18. [15] Izumi ( S. ), Note on convergence and orders of vanishing along curves, Manuscripta math. 66, p. 261-275 (1990). Zbl0711.32002MR1031196
  19. [L-J] Lejeune-Jalabert ( M.), Courbes tracées sur un germe d'hypersurface , Amer. J. Math.112, p. 525-568 (1990). Zbl0743.14002MR1064990
  20. [L-J-T] Lejeune-Jalabert ( M.), Teissier ( B.), Contribution à l'étude des singularités du point de vue du polygone de Newton, thèse université ParisVII (1973). 
  21. [Lo] Looijenga ( E.), Motivic Measures, Séminaire Bourbaki1999/2000874, Astérisque276, p. 267-297 (2002). MR1886763
  22. [N] Nash JR( J.F. ), Arc structure of singularities, Duke Math. Journ.81, p. 31-38 (1995). Zbl0880.14010MR1381967
  23. [P] Pawlucki ( W.), On Gabrielov's regularity condition for analytic mappings, Duke Math. J.65, p. 299-311 (1992). Zbl0773.32009MR1150588
  24. [R1] Reguera ( A.J.), Families of arcs on rational surface singularities , Manuscripta Math.88, p. 321-333 (1995). Zbl0867.14012MR1359701
  25. [R2] Reguera ( A.J.), Image of the Nash map in terms of wedges , C.R. Acad. Sci. Paris, Ser. I338, p. 385-390 (2004). Zbl1044.14032MR2057169
  26. [S] Sebag ( J.) , Intégration motivique sur les schémas formels, à paraître au Bull. S.M.F. (2004). Zbl1084.14012
  27. [T1] Tougeron ( J.C.), Idéaux de fonctions différentiables, Ann. Inst. Fourier18, p. 177-240 (1968). Zbl0188.45102MR240826
  28. [T2] Tougeron ( J.C. ), Idéaux de fonctions différentiables , Ergeb. der Mathematik71, Springer Verlag (1972). Zbl0251.58001MR440598
  29. [T3] Tougeron ( J.C. ), An extension of Whithney's spectral theorem , Pub. Math. I.H.E.S.40, p. 139-148 (1971). MR370645
  30. [T4] Tougeron ( J.C.), Courbes analytiques sur un germe d'espace analytique et applications, Ann. Inst. Fourier26, p. 117-131 (1976). Zbl0318.32005MR414919

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