On isotropic divisors on irreducible symplectic manifolds

Abstract

Let $ X $ be an irreducible symplectic manifold and $ L $ a divisor on $ X $. Assume that $ L $ is isotropic with respect to the Beauville-Bogomolov quadratic form. We define the rational Lagrangian locus and the movable locus on the universal deformation space of the pair $ (X,L) $. We prove that the rational Lagrangian locus is empty or coincides with the movable locus of the universal deformation space.