On the relative cone conjecture for families of IHS manifolds

TL;DR

This paper investigates the relative cone conjecture for families of K-trivial varieties with vanishing irregularity and proves the conjecture for fibrations in projective irreducible holomorphic symplectic (IHS) manifolds of four known deformation types.

Contribution

It establishes the validity of the relative movable and nef cone conjectures for fibrations in projective IHS manifolds of four deformation types.

Findings

Proves the relative cone conjecture for certain IHS fibrations.

Confirms the relative movable and nef cone conjectures in these cases.

Advances understanding of cone structures in IHS manifolds.

Abstract

We study the relative cone conjecture for families of $K$-trivial varieties with vanishing irregularity. As an application we prove that the relative movable and the relative nef cone conjectures hold for fibrations in projective IHS manifolds of the 4 known deformation types.