On the ampleness of positive CR line bundles over Levi-flat manifolds

Abstract

We give an example of a compact Levi-flat CR 3-manifold with a positive-along-leaves CR line bundle which is not ample with respect to transversely infinitely differentiable CR sections. This example shows that we cannot improve the regularity of Kodaira type embedding theorem for compact Levi-flat CR manifolds obtained by Ohsawa and Sibony.

12 pages, final version, to appear in Publications of the Research Institute for Mathematical Sciences

References in corpus (1)

• Solving ${\bar{\partial }}_b$ on hyperbolic laminations

Cited by in corpus (3)

• A global estimate for the Diederich--Fornaess index of weakly pseudoconvex domains
• A local expression of the Diederich--Fornaess exponent and the exponent of conformal harmonic measures
• On the normal bundle of Levi-flat real hypersurfaces