Shafarevich-Tate groups of holomorphic Lagrangian fibrations

Anna Abasheva, Vasily Rogov

Consider a Lagrangian fibration $\ddot{I}€:X\to {\mathbb{P}}^n$ on a hyperkähler manifold $X$. There are two ways to construct a holomorphic family of deformations of $\ddot{I}€$ over $\math…