Abelian fibred holomorphic symplectic manifolds

By Justin Sawon. 2003

64 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b6fa53599c9b2bc7fa92ca1e9b9a2ae56a442d3e

Citations in the corpus

• Projectivity and birational geometry of Bridgeland moduli spaces (2012, unknown): “This appeared in print in articles by Hassett–Tschinkel [27], Huybrechts [26], and Sawon [73], and had been proposed earlier (see [80]).”