Finiteness of the space of n-cycles for a reduced (n − 2)-concave complex space

EPIGA, Volume 1 (2017), Nr. 5 We show that for n ≥ 2 the space of closed n-cycles in a strongly (n − 2)-concave complex space has a natural structure of reduced complex space locally of finite dimension and represents the functor " analytic family of n-cycles " parametrized by Banach analy...

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Bibliographic Details
Published in:	Épijournal de géométrie algébrique Vol. 1
Main Author:	Barlet, Daniel
Format:	Journal Article
Language:	English
Published:	EPIGA 01.09.2017 Association Epiga
Subjects:	32g13 ; 32g10 ; 32f10 ; 32d15 [math.math-ag] mathematics [math]/algebraic geometry [math.ag] [math.math-cv] mathematics [math]/complex variables [math.cv] Algebraic Geometry closed n-cycles Complex Variables f-analytic family of cycles hartogs figure Mathematics strongly q-concave space Closed n-cycles Hartogs figure f-analytic family of cycles strongly q-concave space
ISSN:	2491-6765, 2491-6765
Online Access:	Get full text
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Summary:	EPIGA, Volume 1 (2017), Nr. 5 We show that for n ≥ 2 the space of closed n-cycles in a strongly (n − 2)-concave complex space has a natural structure of reduced complex space locally of finite dimension and represents the functor " analytic family of n-cycles " parametrized by Banach analytic sets. Nous montrons que, pour n ≥ 2, l'espace des n-cycles fermés dans un espace complexe fortement (n − 2)-concave a une structure naturelle d'espace complexe réduit localement de dimension finie et que cet espace représente le foncteur " famille analytique de n-cycles " paramétrée par des ensembles analytiques banachiques.
ISSN:	2491-6765 2491-6765
DOI:	10.46298/epiga.2017.volume1.1521