Speaker
Description
The cone conjecture predicts the shape of the nef and movable cones of certain projective varieties, modulo automorphisms. It is notably known for K3 surfaces, abelian varieties, hyperkähler manifolds, and in a few sporadic cases. Together with standard MMP conjectures, it implies the finiteness of minimal models, which can be used to improve birational boundedness to boundedness for certain classes of varieties.
In this talk, we present a descent result under finite group actions for the cone conjecture. Our result applies to arbitrary finite quotients of products involving abelian varieties and hyperkähler manifolds, as well as to Galois descent over perfect fields for those products. Along the way, we highlight a few properties of convex cones that behave themselves better than the cone conjecture, and that are satisfied by many examples coming from complex algebraic geometry.
