A finiteness theorem for Lagrangian fibrations

TL;DR

This paper proves that under certain natural conditions, there are only finitely many holomorphic Lagrangian fibrations up to deformation, contributing to the classification of these geometric structures.

Contribution

It establishes a finiteness theorem for holomorphic Lagrangian fibrations satisfying specific hypotheses, advancing understanding of their moduli space.

Findings

Finiteness of Lagrangian fibrations up to deformation.

Conditions under which the finiteness holds.

Implications for classification of Lagrangian fibrations.

Abstract

We consider (holomorphic) Lagrangian fibrations X->P^n that satisfy some natural hypotheses. We prove that there are only finitely many such Lagrangian fibrations up to deformation.