Published online by Cambridge University Press: 20 July 2020
The base surface $B$ of a Lagrangian fibration
of a projective, irreducible symplectic fourfold
$X$ is shown to be isomorphic to
$\mathbb{P}^{2}$.
DH is supported by the SFB/TR 45 ‘Periods, Moduli Spaces and Arithmetic of Algebraic Varieties’ of the DFG (German Research Foundation). CX is partially supported by a Chern Professorship of the MSRI (NSF No. DMS-1440140) and by the National Science Fund for Distinguished Young Scholars (NSFC 11425101) ‘Algebraic Geometry’.