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 associating to any such ${\mathcal{X}}_0$ the loop space of a finite-dimensional analytic space which serves as a local moduli space of CR structures close to ${\mathcal{X}}_0$. 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.

Final version. To appear in Crelle's journal

References in corpus (1)

• Foliated Structure of The Kuranishi Space and Isomorphisms of Deformation Families of Compact Complex Manifolds