A Hodge-theoretic proof of Hwang’s theorem on base manifolds of Lagrangian fibrations | Synapse
March 28, 2026Open Access
A Hodge-theoretic proof of Hwang’s theorem on base manifolds of Lagrangian fibrations
Key Points
This research aims to provide a Hodge-theoretic proof of Hwang’s theorem regarding base manifolds of Lagrangian fibrations.
Utilized Hodge theory techniques
Analyzed properties of irreducible holomorphic symplectic manifolds
Examined the conditions for smooth bases in Lagrangian fibrations
Established that smooth bases of Lagrangian fibrations are necessarily projective spaces
Clarified the relationship between algebraic geometry and symplectic structures
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.