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Foliated structure of the Kuranishi space and isomorphisms of deformation families of compact complex manifolds

Laurent Meersseman (2011)

Annales scientifiques de l'École Normale Supérieure

Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of 0 in p , for some p > 0 ) or differentiable (parametrized by an open neighborhood of 0 in p , for some p > 0 ) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point t of the parameter space, the fiber over t of the first family is biholomorphic to the fiber over t of the second family. Then, under which conditions are the...

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