Approximately holomorphic geometry for projective CR manifolds

Details Approximately holomorphic geometry for projective CR manifolds Approximately holomorphic geometry for projective CR manifolds

2006-11-05

arxiv.org/abs/math/0611125v1

Mathematics

Complex Variables

Scientific paper

For compact CR manifolds of hypersurface type which embed in complex projective space, we show for all $k$ large enough the existence of linear systems of $\mathcal{O}(k)$, which when restricted to the CR manifold are generic in a suitable sense. In general these systems are constructed using approximately holomorphic geometry, but for strictly $\mathbb{C}$-convex hypersurfaces generic degree one pencils are obtained via dual geometry. In particular known results about the differential topological type of strictly $\mathbb{C}$-convex hypersurfaces are recovered.

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