Lagrangian fibrations on hyperkahler manifolds have no multiple fibers in codimension one

Source abstract

Let $f:\; M \to {\mathbb C}P^n$ be a Lagrangian fibration on a compact hyperkahler manifold. We prove that $f$ has no multiple fibers in codimension 1. We prove that this condition is equivalent to the primitivity of the fundamental class of $π^{-1}(H)$, where $H \subset {\mathbb C}P^n$ denotes a hyperplane divisor.