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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

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Volume 2019, Issue 749


Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle

Laurent Meersseman
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/crelle-2016-0030


Kuranishi’s fundamental result (1962) associates to any compact complex manifold X0 a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to X0. In this paper, we give an analogous statement for Levi-flat CR-manifolds fibering properly over the circle by associating to any such 𝒳0 the loop space of a finite-dimensional analytic space which serves as a local moduli space of CR-structures close to 𝒳0. We then develop in this context a Kodaira–Spencer deformation theory making clear the likenesses as well as the differences with the classical case. The article ends with applications and examples.


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About the article

Received: 2014-10-12

Revised: 2016-05-03

Published Online: 2016-08-17

Published in Print: 2019-04-01

Funding Source: Agence Nationale de la Recherche

Award identifier / Grant number: ANR-08-JCJC-0130-01

This work was partially supported by project COMPLEXE (ANR-08-JCJC-0130-01) from the Agence Nationale de la Recherche. It is part of Marie Curie project DEFFOL 271141 funded by the European Community.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2019, Issue 749, Pages 87–132, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2016-0030.

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