Jun-Muk Hwang
Base manifolds for fibrations of projective irreducible symplectic manifolds
Abstract: Given a projective irreducible symplectic manifold $M$ of dimension
$2n$, a projective manifold $X$ and a surjective holomorphic map
$f:M \rightarrow X$ with connected fibers of positive dimension, we
prove that $X$ is biholomorphic to the projective space of dimension
$n$. The proof is obtained by exploiting two geometric structures at
general points of $X$: the affine structure arising from the action
variables of the Lagrangian fibration $f$ and the structure defined
by the variety of minimal rational tangents on the Fano manifold $X$.