Characteristic foliation on vertical hypersurfaces on holomorphic symplectic manifolds with Lagrangian Fibration

Abstract

Let $Y$ be a smooth hypersurface in a projective irreducible holomorphic symplectic manifold $X$ of dimension $2n$. The characteristic foliation $F$ is the kernel of the symplectic form restricted to $Y$. Assume that $X$ is equipped with a Lagrangian fibration $\pi :X\to B$ and $Y={\pi }^{-1}D$, where $D$ is a hypersurface in $B$. It is easy to see that the leaves of $F$ are contained in the fibers of $\pi$. We prove that a very general leaf is Zariski dense in a fiber of $\pi$.

In this version we don't need the base of the Lagrangian fibration to be smooth

References in corpus (2)

• Base manifolds for fibrations of projective irreducible symplectic manifolds
• On the characteristic foliation on a smooth hypersurface in a holomorphic symplectic fourfold

Cited by in corpus (1)

• On algebraically coisotropic submanifolds of holomorphic symplectic manifolds