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

2025/12/22 by Aurélien Faucher, Faucher, Aurélien
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2512.19656

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

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.

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Related

• The Morrison--Kawamata cone conjecture for singular symplectic varieties
• On the relative Morrison-Kawamata cone conjecture (II)
• On the relative Morrison-Kawamata cone conjecture
• Well-clipped cones behave themselves under all finite quotients, the cone conjecture under most
• The cone conjecture for some rational elliptic threefolds