On fibre space structures of a projective irreducible symplectic manifold
alg-geom
2016-08-30 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.alg-geom/9709033,
title = {On fibre space structures of a projective irreducible symplectic manifold},
author = {Daisuke Matsushita},
journal= {arXiv preprint arXiv:alg-geom/9709033},
year = {2016}
}