arXiv subjects
Publications and source records attributed to Renat Abugaliev.
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. In this article we prove that a generic leaf of the characteristic foliation is dense in Y if Y has positive Beauville-Bogomolov-Fujiki square.
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 $π:X\to B$ and $Y=π^{-1}D$, where $D$ is a hypersurface in $B$. It is easy to see that the leaves of $F$ are contained in the fibers of $π$. We prove that a very general leaf is Zariski dense in a fiber of $π$.