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Lagrangian fibrations on hyperkahler manifolds

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If you have a question about this talk, please contact Dr. J Ross.

The general fibre of a Lagrangian fibration on a hyperkahler manifold is a Lagrangian torus. It is a question of Beauville whether any Lagrangian torus in a hyperkahler manifold arises in this way.

In my talk, I will describe recent joint work with Christian Lehn and Sonke Rollenske giving a positive answer to Beauville’s question in the non-projective case. Furthermore, I will derive a criterion for the existence of a Lagrangian fibration in the projective case, which has recently been used by Jun-Muk Hwang to provide a positive answer to Beauville’s question for projective hyperkahler manifolds.

This talk is part of the Workshop on Kahler Geometry series.

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