Pullbacks of hyperplane sections for Lagrangian fibrations are primitive

TL;DR

This paper proves that for a Lagrangian fibration on a hyperkähler manifold, the pullback of the generator of the Picard group of the base is a primitive class on the total space.

Contribution

It establishes the primitivity of the pullback of the Picard generator in the context of Lagrangian fibrations on hyperkähler manifolds.

Findings

Pullback of Picard generator is primitive on the total space

Supports structure understanding of hyperkähler Lagrangian fibrations

Advances knowledge of cohomology classes in hyperkähler geometry

Abstract

Let p: M -> B be a Lagrangian fibration on a hyperkahler manifold of maximal holonomy (also known as IHS), and H the generator of the Picard group of B. We prove that the pullback $p^*(H)$ is a primitive class on M.