Aurélien Faucher | Searcharxiv

arXiv2026

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

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.

math.AG↗

arXiv2026

The relative movable cone conjecture for K-trivial fibrations in varieties with well-clipped movable cones

We prove the weak relative Kawamata-Morrison movable cone conjecture for K-trivial fibrations whose very general fibre is a quotient, by a finite group of automorphisms acting freely in codimension one, of a product of certain Calabi-Yau pairs whose underlying varieties have well-clipped movable cones, a notion recently introduced by Cécile Gachet. Our main result applies in particular when the fibre is a finite product of an abelian variety, smooth rational surfaces underlying klt Calabi-Yau pairs, projective irreducible holomorphic symplectic manifolds and Enriques manifolds, both of a known type. As a consequence, there are only finitely many minimal models over the base, up to isomorphism. When the relative movable cone is non-degenerate, we obtain the full relative movable cone conjecture.

math.AG↗