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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.07624 |
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Table of Contents:
- This is a survey article, with essentially complete proofs, of a series of recent results concerning the geometry of the characteristic foliation on smooth divisors in compact hyperkähler manifolds, starting with work by Hwang-Viehweg, but also covering articles by Amerik-Campana and Abugaliev. The restriction of the holomorphic symplectic form on a hyperkähler manifold $X$ to a smooth hypersurface $D\subset X$ leads to a regular foliation ${\mathcal F}\subset{\mathcal T}_D$ of rank one, the characteristic foliation. The picture is complete in dimension four and shows that the behavior of the leaves of ${\mathcal F}$ on $D$ is determined by the Beauville-Bogomolov square $q(D)$ of $D$. In higher dimensions, some of the results depend on the abundance conjecture for $D$.