On fibre space structures of a projective irreducible symplectic manifold

@inproceedings{Matsushita1997OnFS,
  title={On fibre space structures of a projective irreducible symplectic manifold},
  author={Daisuke Matsushita},
  year={1997}
}
In this note, we investigate fibre space structures of a projective irreducible symplectic manifold. We prove that an 2n-dimensional projective irreducible symplectic manifold admits only an n-dimensional fibration over a Fano variety which has only Q-factorial log-terminal singularities and whose Picard number is one. Moreover we prove that a general fibre is an abelian variety up to finite unramified cover, especially, a general fibre is an abelian surface for 4-fold. 
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