The Cone Conjecture for Primitive Symplectic Varieties over a Field of Characteristic Zero and an Application

TL;DR

This paper proves the cone conjecture for certain primitive symplectic varieties over characteristic zero fields and applies it to fibrations with primitive symplectic fibers.

Contribution

It establishes the Kawamata-Morrison cone conjecture for Q-factorial terminal projective primitive symplectic varieties with high second Betti number.

Findings

Proved the cone conjecture for primitive symplectic varieties over characteristic zero.

Validated the relative movable and nef cone conjectures for specific fibrations.

Extended the understanding of symplectic varieties in algebraic geometry.

Abstract

We prove the Kawamata-Morrison cone conjecture for Q-factorial terminal projective primitive symplectic varieties with second Betti number greater than five defined over a field of characteristic zero. As an application, we prove that the relative movable and the relative nef cone conjectures hold for fibrations whose very general fibre is a projective primitive symplectic varieties under certain assumptions.