Beschreibung:
We study monodromy and discriminant locus of Lagrangian fibrations on 4-dimensional Hyperkähler manifolds under the assumption that the fibres are principally polarised and the monodromy is unipotent of rank 1. We prove that group-theoretic properties of Sp(4,Z) lead to integer-valued invariants. Using Matsushitas result on higher direct image sheaves, we prove a formula for the degree of the discriminant locus. We prove that this degree is smaller or equal to 30 provided that the general fibre is irreducible as a principally polarised abelian variety. Further we discuss a possible construction of a Lagrangian fibration with discriminant locus of degree 26.