Abelian fibred holomorphic symplectic manifolds
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.
Anahtar Kelimeler:
Turk. J. Math., 27, (2003), 197-230. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.27, iss.1.
Abelian fibred holomorphic symplectic manifolds
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.
Keywords:
Turk. J. Math., 27, (2003), 197-230. Full text: pdf Other articles published in the same issue: Turk. J. Math., vol.27, iss.1.,
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
Sayıdaki Diğer Makaleler
U(1)-invariant special Lagrangian 3-folds in {\mathbb C}3 and special Lagrangian fibrations
A monopole homology for integral homology 3-spheres
Galois symmetry on Floer cohomology
Comparing open book and Heegaard decompositions of 3-manifolds
Polyhedral approximations of Riemannian manifolds
On cofinite subgroups of mapping class groups
Duality and Fibrations on G2 Manifolds
Abelian fibred holomorphic symplectic manifolds
Affine Manifolds, Log Structures, and Mirror Symmetry