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.

Source : oai:HAL:hal-01184765v2

Volume: Volume 1

Published on: September 1, 2017

Submitted on: July 12, 2017

Keywords: Closed n-cycles,strongly q-concave space,Hartogs figure,f-analytic family of cycles,32G13 ; 32G10 ; 32F10 ; 32D15,[MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV],[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]

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