A note on the one-dimensional systems of formal equations
Annales de l'Institut Fourier, Tome 39 (1989) no. 3, p. 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},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {39},
     number = {3},
     year = {1989},
     pages = {633-640},
     doi = {10.5802/aif.1179},
     zbl = {0705.14003},
     mrnumber = {91b:14002},
     language = {en},
     url = {http://http://www.numdam.org/item/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/item/AIF_1989__39_3_633_0/

[A] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES, 36 (1969), 23-58. | Numdam | MR 42 #3087 | Zbl 0181.48802

[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 87g:14023 | Zbl 0612.14020

[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 19,881b | Zbl 0099.15702

[K] D. Kirby, The reduction number of a one-dimensional local ring, J. London Math. Soc., (2) 10 (1975), 471-481. | MR 52 #388 | Zbl 0305.13017

[La] D. Lascar, Caractère effectif des théorèmes d'approximation d'Artin, CRAS, 287 (1978), 907-910. | MR 80c:14006 | Zbl 0424.13005

[Le] M. Lejeune-Jalabert, Courbes tracées sur un germe d'hypersurface. Preprint. | Zbl 0743.14002

[M] E. Matlis, E.1-Dimensional Cohen-Macaulay Rings, Lecture Notes in Math. n° 327, Springer Verlag, 1977. | Zbl 0264.13012

[N] J. Nash, Arc structure of singularities. Preprint. | Zbl 0880.14010

[VdW] B. Van Der Waerden, Infinitely near points, Indagationes Math., 12 (1950), 401-410. | MR 12,527c | Zbl 0038.32101

[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 52 #8488 | Zbl 0303.32018

[W2] J.J. Wavrik, Analytic equations and singularities of plane curves, Trans. A.M.S., 245 (1978), 409-417. | MR 80a:14004 | Zbl 0403.13009