Characteristic foliation on hypersurfaces with positive Beauville-Bogomolov-Fujiki square (Q6623535)

Let \(Y\) be a smooth hypersurface in a projective irreducible holomorphic symplectic manifold \(X\) of dimension \(2n\) over \(\mathbb{C}\). The manifold \(X\) satisfies the following properties: \N\begin{itemize}\N\item[1)] \(H^0(X, \Omega_X^2) =\mathbb{C}\sigma\), where \(\sigma\) is a holomorphic symplectic form (at any point of \(X\)); \N\item[2)] \(H^1(X,\mathcal{O}_X)=0\); \N\item[3)] \(\pi_1(X)=0\). \N\end{itemize}\NThe characteristic foliation \(F\) is the kernel of the symplectic form restricted to \(Y\). The author proves that a generic leaf of the characteristic foliation is dense in \(Y\) if \(Y\) has positive Beauville-Bogomolov-Fujiki square.