Characteristic foliation on a hypersurface of general type in a projective symplectic manifold

Abstract

Given a projective symplectic manifold $M$ and a non-singular hypersurface $X\subset M$, the symplectic form of $M$ induces a foliation of rank 1 on $X$, called the characteristic foliation. We study the question when the characteristic foliation is algebraic, namely, all the leaves are algebraic curves. Our main result is that the characteristic foliation of $X$ is not algebraic if $X$ is of general type. For the proof, we first establish an étale version of Reeb stability theorem in foliation theory and then combine it with the positivity of the direct image sheaves associated to families of curves.

Cited by in corpus (2)

• Codimension one foliations with numerically trivial canonical class on singular spaces
• Foliated affine and projective structures