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 the Kodaira type embedding theorem for compact Levi-flat CR manifolds obtained by Ohsawa and Sibony.
Cite this article
Masanori Adachi, On the Ampleness of Positive CR Line Bundles over Levi-flat Manifolds. Publ. Res. Inst. Math. Sci. 50 (2014), no. 1, pp. 153–167DOI 10.4171/PRIMS/127