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

Abstract : Kuranishi's fundamental result (1962) associates to any compact complex manifold $X_0$ a finite-dimensional analytic space which has to be thought of as a local moduli space of complex structures close to $X_0$. In this paper, we give an analogous statement for Levi-flat CR manifolds fibering properly over the circle by describing explicitely an infinite-dimensional Kuranishi type local moduli space of Levi-flat CR structures. We interpret this result in terms of 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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Journal articles

https://hal.archives-ouvertes.fr/hal-00738787
Contributor : Laurent Meersseman Connect in order to contact the contributor
Submitted on : Friday, October 5, 2012 - 10:24:40 AM
Last modification on : Friday, November 25, 2022 - 10:12:06 AM

### Citation

Laurent Meersseman. Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle. Journal für die reine und angewandte Mathematik, 2019, 749, pp.87-132. ⟨10.1515/crelle-2016-0030⟩. ⟨hal-00738787⟩

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