Zariski F-decomposition and Lagrangian fibration on hyperkähler manifolds

Abstract

For a compact hyperkähler manifold X, we show certain Zariski decomposition for every pseudo-effective R-divisor, and give a sufficient condition for X to be bimeromorphic to a (holomorphic) Lagrangian fibration. We also prove that any sequence of D-flops between projective hyperkähler manifolds terminates after finite steps.

arXiv commentSimplified the proof of Theorem 4.1. Final arXiv version