Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations
Annales de l'Institut Fourier, Tome 50 (2000) no. 4, pp. 1155-1189.

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.

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.

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     title = {Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations},
     journal = {Annales de l'Institut Fourier},
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Mathieu, David. Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations. Annales de l'Institut Fourier, Tome 50 (2000) no. 4, pp. 1155-1189. doi : 10.5802/aif.1788. http://www.numdam.org/articles/10.5802/aif.1788/

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