no. 3
A note on the one-dimensional systems of formal equations
Annales de l'Institut Fourier, Tome 39 (1989) no. 3, pp. 633-640.

Dans cet article, on calcule la fonction β du théorème d’approximation de M. Artin pour les systèmes d’équations formelles de dimension un.

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

@article{AIF_1989__39_3_633_0,
     author = {Elias, Juan},
     title = {A note on the one-dimensional systems of formal equations},
     journal = {Annales de l'Institut Fourier},
     pages = {633--640},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {39},
     number = {3},
     year = {1989},
     doi = {10.5802/aif.1179},
     mrnumber = {91b:14002},
     zbl = {0705.14003},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1179/}
}
TY  - JOUR
AU  - Elias, Juan
TI  - A note on the one-dimensional systems of formal equations
JO  - Annales de l'Institut Fourier
PY  - 1989
SP  - 633
EP  - 640
VL  - 39
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.1179/
DO  - 10.5802/aif.1179
LA  - en
ID  - AIF_1989__39_3_633_0
ER  - 
%0 Journal Article
%A Elias, Juan
%T A note on the one-dimensional systems of formal equations
%J Annales de l'Institut Fourier
%D 1989
%P 633-640
%V 39
%N 3
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.1179/
%R 10.5802/aif.1179
%G en
%F AIF_1989__39_3_633_0
Elias, Juan. A note on the one-dimensional systems of formal equations. Annales de l'Institut Fourier, Tome 39 (1989) no. 3, pp. 633-640. doi : 10.5802/aif.1179. http://www.numdam.org/articles/10.5802/aif.1179/

[A] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES, 36 (1969), 23-58. | Numdam | MR | Zbl

[Ca] E. Casas, Sobre el cálculo efectivo del género de las curvas algebraicas, Collect. Math., 25 (1974), 3-11.

[E] J. Elias, On the analytic equivalence of curves, Proc. Camb. Phil. Soc., 100, 1(1986), 57-64. | MR | Zbl

[ECh] F. Enriques and O. Chisini, Teoria geometrica delle equazione e delle funzione algebriche. Nicola Zanichelli, Bologna 1918.

[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). | MR | Zbl

[K] D. Kirby, The reduction number of a one-dimensional local ring, J. London Math. Soc., (2) 10 (1975), 471-481. | MR | Zbl

[La] D. Lascar, Caractère effectif des théorèmes d'approximation d'Artin, CRAS, 287 (1978), 907-910. | MR | Zbl

[Le] M. Lejeune-Jalabert, Courbes tracées sur un germe d'hypersurface. Preprint. | Zbl

[M] E. Matlis, E.1-Dimensional Cohen-Macaulay Rings, Lecture Notes in Math. n° 327, Springer Verlag, 1977. | Zbl

[N] J. Nash, Arc structure of singularities. Preprint. | Zbl

[VdW] B. Van Der Waerden, Infinitely near points, Indagationes Math., 12 (1950), 401-410. | MR | Zbl

[W1] J.J. Wavrik, A theorem on solutions of Analytic equations with applications to deformations of complex structures, Math. Ann., 216 (1975), 127-142. | MR | Zbl

[W2] J.J. Wavrik, Analytic equations and singularities of plane curves, Trans. A.M.S., 245 (1978), 409-417. | MR | Zbl

Cité par Sources :