Relations among analytic functions. II
Annales de l'Institut Fourier, Volume 37 (1987) no. 2, p. 49-77
This is a sequel to “Relations among analytic functions I”, Ann. Inst. Fourier, 37, fasc. 1, [pp. 187-239]. We reduce to semicontinuity of local invariants the problem of finding 𝒞 solutions to systems of equations involving division and composition by analytic functions. We prove semicontinuity in several general cases : in the algebraic category, for “regular” mappings, and for module homomorphisms over a finite mapping.
Cet article fait suite à “Relations among analytic functions I”, Ann. Inst. Fourier, 37, fasc. 1, [pp. 187-239]. On réduit à la semicontinuité des invariants locaux le problème de trouver des solutions 𝒞 de systèmes d’équations dans lesquelles interviennent division et composition par des fonctions analytiques. On démontre la semicontinuité dans plusieurs cas généraux : dans la catégorie algébrique, pour les morphismes “réguliers”, et pour les holomorphismes de modules sur un morphisme fini.
@article{AIF_1987__37_2_49_0,
     author = {Bierstone, Edward and Milman, P. D.},
     title = {Relations among analytic functions. II},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {37},
     number = {2},
     year = {1987},
     pages = {49-77},
     doi = {10.5802/aif.1086},
     zbl = {0611.32003},
     mrnumber = {88g:32013b},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1987__37_2_49_0}
}
Bierstone, Edward; Milman, P. D. Relations among analytic functions. II. Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 49-77. doi : 10.5802/aif.1086. http://www.numdam.org/item/AIF_1987__37_2_49_0/