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

2019/09/16 by Abugaliev, Renat
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.07260

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 π:X→ B and Y=π^-1D, 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.

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