Parabolic nef currents on hyperkaehler manifolds

Details Parabolic nef currents on hyperkaehler manifolds Parabolic nef currents on hyperkaehler manifolds

2009-07-24

arxiv.org/abs/0907.4217v4

Mathematics

Complex Variables

v. 4.0, 22 pages, some inaccuracies in section 3.3 are corrected

Scientific paper

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.

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