Finiteness of isomorphism classes of generic fibers in pointed locally trivial families of Q-factorial terminal primitive symplectic varieties with fixed special fiber, plus projective finiteness under semi-ampleness, with optimality via explicit infinite families.
The Cone Conjecture for Primitive Symplectic Varieties over a Field of Characteristic Zero and an Application
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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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Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture
Finiteness of isomorphism classes of generic fibers in pointed locally trivial families of Q-factorial terminal primitive symplectic varieties with fixed special fiber, plus projective finiteness under semi-ampleness, with optimality via explicit infinite families.