Abelian fibred holomorphic symplectic manifolds

Details Abelian fibred holomorphic symplectic manifolds Abelian fibred holomorphic symplectic manifolds

2004-04-20

arxiv.org/abs/math/0404362v1

Turkish J. Math. 27 (2003), no. 1, 197-230

Mathematics

Algebraic Geometry

34 pages, for the Proceedings of the 9th Gokova Geometry-Topology Conference (2002), uses gokova.cls and goksty.tex

Scientific paper

We study holomorphic symplectic manifolds which are fibred by abelian varieties. This structure is a higher dimensional analogue of an elliptic fibration on a K3 surface. We investigate when a holomorphic symplectic manifold is fibred in this way, and are led to several natural conjectures. We then study the geometry of these fibrations. The expectation is that this point of view will prove useful in understanding holomorphic symplectic manifolds, and possibly lead to a classification.

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