Foliations on hypersurfaces in holomorphic symplectic manifolds

Abstract:

Let Y be a hypersurface in a 2n-dimensional holomorphic symplectic manifold X. The restriction \sigma|_Y of the holomorphic symplectic form induces a rank one foliation on Y. We investigate situations where this foliation has compact leaves; in such cases we obtain a space of leaves Y/F which has dimension 2n-2 and admits a holomorphic symplectic form.

Appears in (2009) No. 23 of International Mathematics Research Notices. Available as arXiv:0812.3939 from the e-Print archive.

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