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Convexité holomorphe intermediaire

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Abstract

The purpose of the present article is to give a generalisation of the notion of holomorphic convexity. We begin with an analogue of Remmert's reduction Theorem by showing that aq-holomorphically convex complex space is naturally endowed with a proper morphism on aq-complete space. We show after that theq-complete spaces arising in this situation are special: they enjoy in particular the property that each relatively compact open subset carries a Kähler form.

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Authors and Affiliations

  1. Institut E. Cartan, CNRS UA750, Université de Nancy I, F-54506, Vandoeuvre-les-Nancy, France

    Daniel Barlet

  2. Dipartimento di Matematica G. Castelnuovo, Universitá di Roma La Sapienza, Roma, Italy

    Alessandro Silva

Authors
  1. Daniel Barlet
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  2. Alessandro Silva
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Additional information

Une grande partie de cet article a été conçue lors d'un sejour du premier auteur à l'Université de Rome “La Sapienza”; celui-ci tient à remercier le CNR et le Départment G. Castelnuovo

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Barlet, D., Silva, A. Convexité holomorphe intermediaire. Math. Ann. 296, 649–665 (1993). https://doi.org/10.1007/BF01445127

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  • DOI: https://doi.org/10.1007/BF01445127

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