On fibre space structures of a projective irreducible symplectic manifold

Details On fibre space structures of a projective irreducible symplectic manifold On fibre space structures of a projective irreducible symplectic manifold

1997-09-30

arxiv.org/abs/alg-geom/9709033v1

Mathematics

Algebraic Geometry

Scientific paper

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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