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

Laurent Meersseman EMAIL logo

Abstract

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.

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

Funding statement: 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.

Acknowledgements

I enjoyed the warm atmosphere of the CRM of Bellaterra during the elaboration of this work. I would like to thank the ANR, the CRM and the European Community. This work benefited from fruitful discussions with Marcel Nicolau to whom I am especially grateful.

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Received: 2014-10-12
Revised: 2016-05-03
Published Online: 2016-08-17
Published in Print: 2019-04-01

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