On the Characteristic Foliation on a Smooth Hypersurface in a Hyperkaehler Manifold

Student: Abugaliev Renat

Educational Programme: Mathematics (Master)

Year of Graduation: 2018

Let $D$ be a smooth divisor on an irreducible holomorphic symplectic variety. The characteristic foliation $F$ is the kernel of the symplectic form restricted to $D$. Assume $\pi:X\to \pr^{n}$ is a Lagrangian fibration and $D=\pi^{-1}Y$, where $Y$ is a divisor on $\pr^{n}$. It is easy to see that the leafs of $F$ are contained in the fibers of $\pi$. One can conjecture that a general leaf is Zariski dense in a fiber of $\pi$. We prove this conjecture under some certain assumption. In particular we prove it for an isotrivial fibration $\pi$.

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