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 coincide with the movable locus.

References in corpus (3)

• Bridgeland's stability and the positive cone of the moduli spaces of stable objects on an abelian surface
• Families of Lagrangian fibrations on hyperkaehler manifolds
• On almost holomorphic Lagrangian fibrations

Cited by in corpus (7)

• Monodromy Invariants and Polarization Types of Generalized Kummer Fibrations
• A proof of the Kawamata-Morrison Cone Conjecture for holomorphic symplectic varieties of K3^[n] or generalized Kummer deformation type
• Criteria for the existence of equivariant fibrations on algebraic surfaces and hyperkähler manifolds and equality of automorphisms up to powers - a dynamical viewpoint
• Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds
• Special Kähler geometry and holomorphic Lagrangian fibrations
• On the non-divisorial base locus of big and nef line bundles of K3^{[2]}-type varieties
• Lagrangian fibrations on symplectic fourfolds