Base manifolds for Lagrangian fibrations on hyperk\"ahler manifolds

TL;DR

This paper proves that the base of a Lagrangian fibration on a hyperk"ahler manifold is always complex projective space, extending previous results to the broader K"ahler setting.

Contribution

It generalizes Hwang's theorem by showing the base manifold is complex projective space for Lagrangian fibrations on hyperk"ahler manifolds.

Findings

Base manifold is isomorphic to complex projective space

Extension of Hwang's theorem to K"ahler case

Broader understanding of hyperk"ahler fibrations

Abstract

We show that the base manifold of a Lagrangian fibration on a hyperk\"ahler manifold is isomorphic to complex projective space. This generalises a theorem of J.-M. Hwang to the K\"ahler case.