Finiteness of Lagrangian fibrations with fixed invariants

TL;DR

This paper proves the finiteness of hyperkähler Lagrangian fibrations with fixed invariants, such as dimension, Fujiki constant, and discriminant, up to deformation, and also with a specified ample line bundle degree.

Contribution

It establishes the first finiteness results for hyperkähler Lagrangian fibrations with fixed invariants and line bundle degrees.

Findings

Finiteness of hyperkähler Lagrangian fibrations with fixed invariants

Finiteness with a given degree of an ample line bundle on fibers

Results hold up to deformation

Abstract

We prove finiteness of hyperkaehler Lagrangian fibrations in any fixed dimension with fixed Fujiki constant and discriminant of the Beauville-Bogomolov-Fujiki lattice, up to deformation. We also prove finiteness of hyperk\"ahler Lagrangian fibrations with an ample line bundle of a given degree on the general fiber of the fibration.