Birational boundedness for holomorphic symplectic varieties and Zarhin's trick for K3 surfaces

Abstract: K3 surfaces are the simply connected projective surfaces with trivial
canonical bundle. These come with a degree which can take any positive even
integer value. K3 surfaces of unbounded degree do not form a bounded
family, ie, there is no scheme of finite type that parametrizes all K3
surfaces. We will explain how to construct birationally bounded families of
holomorphic symplectic varieties associated to K3 surfaces of unbounded
degree, and will give some applications.