Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle - Archive ouverte HAL Access content directly
Journal Articles Journal für die reine und angewandte Mathematik Year : 2019

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.

Dates and versions

hal-00738787 , version 1 (05-10-2012)

Identifiers

Cite

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⟩
141 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More