Let be a complex projective Hyperkähler manifold. By a recent result of Höring and Peternell, the cotangent bundle of is not pseudoeffective. One way to measure this negativity more precisely is to give sufficient conditions on an ample line bundle such that the twist is pseudoeffective. I will give a sufficient condition that depends only on the deformation’s type of . Then I will discuss when this sufficient condition is also necessary. At the end I’ll briefly present some recent progress on the case of degree two K3 surfaces. This is a joint work with Andreas Höring.
