A note on the one-dimensional systems of formal equations

Juan Elias

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 3, page 633-640
  • ISSN: 0373-0956

Abstract

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On this paper we compute the numerical function β of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.

How to cite

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Elias, Juan. "A note on the one-dimensional systems of formal equations." Annales de l'institut Fourier 39.3 (1989): 633-640. <http://eudml.org/doc/74843>.

@article{Elias1989,
abstract = {On this paper we compute the numerical function $\beta $ of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.},
author = {Elias, Juan},
journal = {Annales de l'institut Fourier},
keywords = {Artin approximation; system of formal equations; algebroid curve},
language = {eng},
number = {3},
pages = {633-640},
publisher = {Association des Annales de l'Institut Fourier},
title = {A note on the one-dimensional systems of formal equations},
url = {http://eudml.org/doc/74843},
volume = {39},
year = {1989},
}

TY - JOUR
AU - Elias, Juan
TI - A note on the one-dimensional systems of formal equations
JO - Annales de l'institut Fourier
PY - 1989
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 3
SP - 633
EP - 640
AB - On this paper we compute the numerical function $\beta $ of the approximation theorem of M. Artin for the one-dimensional systems of formal equations.
LA - eng
KW - Artin approximation; system of formal equations; algebroid curve
UR - http://eudml.org/doc/74843
ER -

References

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  1. [A] M. ARTIN, Algebraic approximation of structures over complete local rings, Publ. Math. IHES, 36 (1969), 23-58. Zbl0181.48802MR42 #3087
  2. [Ca] E. CASAS, Sobre el cálculo efectivo del género de las curvas algebraicas, Collect. Math., 25 (1974), 3-11. 
  3. [E] J. ELIAS, On the analytic equivalence of curves, Proc. Camb. Phil. Soc., 100, 1(1986), 57-64. Zbl0612.14020MR87g:14023
  4. [ECh] F. ENRIQUES and O. CHISINI, Teoria geometrica delle equazione e delle funzione algebriche. Nicola Zanichelli, Bologna 1918. 
  5. [H] H. HIRONAKA, On the arithmetic genera and the effective genera of algebraic curves. Memoirs of the College of Sciences, Univ. Tokyo, Ser.A, Vol.XXX, Math., n° 2(1957). Zbl0099.15702MR19,881b
  6. [K] D. KIRBY, The reduction number of a one-dimensional local ring, J. London Math. Soc., (2) 10 (1975), 471-481. Zbl0305.13017MR52 #388
  7. [La] D. LASCAR, Caractère effectif des théorèmes d'approximation d'Artin, CRAS, 287 (1978), 907-910. Zbl0424.13005MR80c:14006
  8. [Le] M. LEJEUNE-JALABERT, Courbes tracées sur un germe d'hypersurface. Preprint. Zbl0743.14002
  9. [M] E. MATLIS, E.1-Dimensional Cohen-Macaulay Rings, Lecture Notes in Math. n° 327, Springer Verlag, 1977. Zbl0264.13012
  10. [N] J. NASH, Arc structure of singularities. Preprint. Zbl0880.14010
  11. [VdW] B. Van der WAERDEN, Infinitely near points, Indagationes Math., 12 (1950), 401-410. Zbl0038.32101MR12,527c
  12. [W1] J.J. WAVRIK, A theorem on solutions of Analytic equations with applications to deformations of complex structures, Math. Ann., 216 (1975), 127-142. Zbl0303.32018MR52 #8488
  13. [W2] J.J. WAVRIK, Analytic equations and singularities of plane curves, Trans. A.M.S., 245 (1978), 409-417. Zbl0403.13009MR80a:14004

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