Parabolic nef currents on hyperkaehler manifolds

Abstract

Let M be a compact, holomorphically symplectic Kahler manifold, and $\eta$ a (1,1)-current which is nef (a limit of Kahler forms). Assume that the cohomology class of $\eta$ is parabolic, that is, its top power vanishes. We prove that all Lelong sets of $\eta$ are coisotropic. When M is generic, this is used to show that all Lelong numbers of $\eta$ vanish. We prove that any hyperkahler manifold with Pic(M) of rank 1 has non-trivial coisotropic subvarieties, if a generator of Pic(M) is parabolic.

18 pages, minor changes, typos corrected, bibliography updated

References in corpus (2)

• Base manifolds for fibrations of projective irreducible symplectic manifolds
• Non-algebraic Hyperkaehler manifolds

Cited by in corpus (2)

• A global Torelli theorem for hyperkahler manifolds
• Families of Lagrangian fibrations on hyperkaehler manifolds