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Relations d'équivalence méromorphes et familles analytiques de cycles

Abstract : The aim of this work is to provide with a finite dimensional complex-analytic structure some subsets of the set [C loc [eta]]([dzéta]) of all [eta]-cycles of a complex-analytic space [dzéta]. First of all, we study the subset of [C loc [eta]]([dzéta]) described by an analytic family of [eta]-cycles parametrized by a finite dimensional, weakly normal complex-analytic space S. We show that, under some assumptions of regularity, there exists a finite dimensional complex-analytic space Q which gives an universal reparametrization of this family. A major step of the proof is a Direct Image Theorem for semi-proper maps with values in infinite dimension al complex-analytic spaces. We explain by the way the link between this result and analytic equivalence relations : the space Q we build is indeed the quotient of S by the equivalence relation defined by the family of cycles. Then, we introduce the concept of meromorphic family of [eta]-cycles of [dzéta] para- metrized by S, for which we give again a theorem of universal reparametrization. We give also a concrete criterion so that an analytic subset of S x [dzéta] may define such a family.
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Submitted on : Thursday, March 29, 2018 - 10:50:11 AM
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Mathieu David. Relations d'équivalence méromorphes et familles analytiques de cycles. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1999. Français. ⟨NNT : 1999NAN10015⟩. ⟨tel-01747051⟩



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