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Variétés d'Albanese supérieures complexes d'une variété kahlérienne compacte

Abstract : In our thesis we present the construction of the higher Albanese manifolds of a kahler compact manifold. These manifolds (whose fundamental groups are the nilpotent quotients without torsion of [pi](X)) are a generalization of the usual AI-banese manifold (whose fundamental group is the abelianization of [pi](X)). We explain two methods of describing them, using the Malcev Lie group of [pi](X). The fisrt approach, inspired by Hain, relies on the existence of a Mixed Hodge Structure on the ring of the group [pi] (X). The second one, inspired by Morgan, involves Sullivan's theory of minimal models (translated to our context). Both deeply use Chen's theory of iterated integrals. After constructing the higher Albanese manifolds (and morphisms), we give some properties and describe the case when X is a curve. Finally, the Albanese manifolds allow us on the one hand to pro ove the holomorphie convexity of the Malcev covering of X. This result is a step towards Shafarevich's conjecture. On the other hand, we describe the vector space of holomorphie functions with polynomial growth of a given rate on the nilpotent galois coverings of X, and this thanks to polynomials on the universal covering of the Albanese manifolds.
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Submitted on : Thursday, March 29, 2018 - 10:50:19 AM
Last modification on : Monday, January 18, 2021 - 1:22:34 PM

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  • HAL Id : tel-01747060, version 1



Sandrine Leroy-Lelièvre. Variétés d'Albanese supérieures complexes d'une variété kahlérienne compacte. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1999. Français. ⟨NNT : 1999NAN10032⟩. ⟨tel-01747060⟩



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