Roundness of the ample cone and existence of double Lagrangian fibrations on hyperkahler manifolds

Ljudmila Kamenova, Misha Verbitsky

Let $M$ be a hyperkahler manifold of maximal holonomy (that is, an IHS manifold), and let $K$ be its Kahler cone, which is an open, convex subset in the space $H^{1,1}(M,R)$ of re…