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Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations

David Mathieu (2000)

Annales de l'institut Fourier

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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