English

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

Algebraic Geometry 2026-05-12 v3

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.

Keywords

Cite

@article{arxiv.2512.19656,
  title  = {The Cone Conjecture for Primitive Symplectic Varieties over a Field of Characteristic Zero and an Application},
  author = {Aurélien Faucher},
  journal= {arXiv preprint arXiv:2512.19656},
  year   = {2026}
}

Comments

28 pages; C\'ecile Gachet has informed us that Theorem A is in fact a consequence of her preprint "Well-clipped cones under finite quotients and applications to the cone conjecture". The introduction has been revised to acknowledge this fact