A Hodge-theoretic proof of Hwang's theorem on base manifolds of Lagrangian fibrations

TL;DR

This paper provides a Hodge-theoretic proof of Hwang's theorem, demonstrating that the base of a Lagrangian fibration of an irreducible holomorphic symplectic manifold is projective space if smooth.

Contribution

It introduces a novel Hodge-theoretic approach to prove a key geometric property of Lagrangian fibrations' bases.

Findings

The base of a Lagrangian fibration is projective space when smooth.

Hodge theory can be used to prove geometric theorems about symplectic manifolds.

The proof offers new insights into the structure of holomorphic symplectic fibrations.

Abstract

We give a Hodge-theoretic proof of Hwang's theorem, which says that if the base of a Lagrangian fibration of an irreducible holomorphic symplectic manifold is smooth, it must be projective space.