Cycle spaces
Espaces des cycles

13 – 24 May 2019
During our stay at the CIRM we intend to finish correcting the second volume of our book on cycle spaces (600 pages approximately). This second volume was submitted in January 2018 to the SMF for publication in the series « Cours Spécialisés” and we are presently waiting for the report of the referee. The first volume has already been published by the SMF in the series Cours spécialisés (no. 22). The title of this first volume is Cycles analytiques complexes I : théorèmes de préparation des cycles – ISBN 1284-6090.
Here is the table of contents for the second volume:
V Construction de l’espace des cycles
VI Classes fondamentales relatives
VII Théorie d’intersection
VIII Espaces quasi-lisses
IX Variété de Chow et espace des cycles
IX L’espace de Douady et l’espace des cycles
XI Convexité holomorphe de l’espace des cycles
XII Kähleriennité de l’espace des cycles
We shall also work on a new paper on the use of non compact cycles in complex geometry. The main idea is to study holomorphic surjective (non proper) maps whose fibres form an analytic (or meromorphic) family of cycles. Good understanding of such mappings is important for the building of non proper meromorphic quotients in complex geometry (see 20, 27 and 32 in the references below), since there is no « universal finite dimensional complex space” classifying the corresponding non compact cycles in a given complex space.

Daniel Barlet (Université de Lorraine)
Jón Ingólfur Magnússon (University of Iceland)