Stability of coisotropic fibrations on holomorphic symplectic manifolds

TL;DR

This paper studies the stability of coisotropic fibrations on holomorphic symplectic manifolds, extending Voisin's results on Lagrangian subvarieties, with applications to moduli spaces of specific deformation types.

Contribution

It generalizes Voisin's stability results from Lagrangian subvarieties to coisotropic fibrations on holomorphic symplectic manifolds.

Findings

Established stability criteria for coisotropic fibrations.

Extended Voisin's results to a broader class of fibrations.

Applied findings to moduli spaces of specific symplectic manifolds.

Abstract

We investigate the stability of fibers of coisotropic fibrations on holomorphic symplectic manifolds and generalize Voisin's result on Lagrangian subvarieties to this framework. We present applications to the moduli space of holomorphic symplectic manifolds which are deformations equivalent to Hilbert schemes of points on a $K3$ surface or to generalized Kummer manifolds.