The generic fiber of a Lagrangian fibration is an abelian variety. This fact is used to associate to each Lagrangian fibration a polarization type which comes from a polarization on a generic fiber. It follows that this polarization type stays constant in a family of Lagrangian fibrations i.e. it is a deformation invariant. Conjecturally the polarization type should only depend on the deformation type of the total space. Indeed, we prove that the polarization type of K3^[n]-type fibrations is always principal.
Fourier-Mukai transforms of line bundles on derived equivalent abelian varieties
A fixed point formula of Lefschetz type in Arakelov geometry IV: the modular height of C.M. abelian varieties
Some elementary theorems about divisibility of 0-cycles on abelian varieties defined over finite fields
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