Characteristic foliation on hypersurfaces with positive Beauville-Bogomolov-Fujiki square

TL;DR

This paper proves that for a generic hypersurface with positive Beauville-Bogomolov-Fujiki square in a holomorphic symplectic manifold, the characteristic foliation's leaves are dense in the hypersurface.

Contribution

It establishes a density property of characteristic foliation leaves on hypersurfaces with positive Beauville-Bogomolov-Fujiki square.

Findings

Generic leaves of the characteristic foliation are dense in the hypersurface.

The result applies to smooth hypersurfaces in irreducible holomorphic symplectic manifolds.

Positive Beauville-Bogomolov-Fujiki square is key to the density property.

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. 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.