Lagrangian fibrations on hyperkahler manifolds (Daniel Greb)

Duration: 51 mins 25 secs

Description:	(No description)

Created:

2012-04-24 09:10

Collection:

Workshop on Kahler Geometry

Publisher:

University of Cambridge

Dr J. Ross

Language:

eng (English)

Credits:

Author:

Daniel Greb


Abstract:	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.

Abstract:

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.

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