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 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 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}, pages = {49--77}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {37}, number = {2}, year = {1987}, doi = {10.5802/aif.1086}, mrnumber = {88g:32013b}, zbl = {0611.32003}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1086/} }
TY - JOUR AU - Bierstone, Edward AU - Milman, P. D. TI - Relations among analytic functions. II JO - Annales de l'Institut Fourier PY - 1987 SP - 49 EP - 77 VL - 37 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1086/ DO - 10.5802/aif.1086 LA - en ID - AIF_1987__37_2_49_0 ER -
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/articles/10.5802/aif.1086/
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