Abelian fibred holomorphic symplectic manifolds

Abstract

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.

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

References in corpus (8)

• Lectures on Special Lagrangian Submanifolds
• Irreducibility of moduli spaces of vector bundles on K3 surfaces
• The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface
• Moduli spaces of hyperkaehler manifolds and mirror symmetry
• Higher dimensional Zariski decompositions
• Rank 2 integrable systems of Prym varieties
• Higher direct images of Lagrangian fibrations
• A new six dimensional irreducible symplectic variety

Cited by in corpus (6)

• Rational Lagrangian fibrations on punctual Hilbert schemes of K3 surfaces
• Kobayashi pseudometric on hyperkahler manifolds
• Families of Lagrangian fibrations on hyperkaehler manifolds
• Higher-dimensional analogues of K3 surfaces
• Moduli spaces of sheaves on K3 surfaces
• On one stable birational invariant