We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.
Nous étudions des familles analytiques de cycles non-compacts, et prouvons qu’il existe un espace analytique de dimension finie, qui fournit une reparamétrisation universelle d’une telle famille, sous certaines conditions de régularité. Nous démontrons ensuite un résultat analogue pour les familles méromorphes de cycles non-compacts. C’est une nouvelle approche des résultats de Grauert sur les relations d’équivalence méromorphes.
@article{AIF_2000__50_4_1155_0, author = {Mathieu, David}, title = {Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations}, journal = {Annales de l'Institut Fourier}, pages = {1155--1189}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {4}, year = {2000}, doi = {10.5802/aif.1788}, mrnumber = {2002c:32011}, zbl = {0966.32003}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1788/} }
TY - JOUR AU - Mathieu, David TI - Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations JO - Annales de l'Institut Fourier PY - 2000 SP - 1155 EP - 1189 VL - 50 IS - 4 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1788/ DO - 10.5802/aif.1788 LA - en ID - AIF_2000__50_4_1155_0 ER -
%0 Journal Article %A Mathieu, David %T Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations %J Annales de l'Institut Fourier %D 2000 %P 1155-1189 %V 50 %N 4 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1788/ %R 10.5802/aif.1788 %G en %F AIF_2000__50_4_1155_0
Mathieu, David. Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations. Annales de l'Institut Fourier, Volume 50 (2000) no. 4, pp. 1155-1189. doi : 10.5802/aif.1788. http://archive.numdam.org/articles/10.5802/aif.1788/
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