Proves finiteness of isomorphism classes of hyper-Kähler varieties in a given deformation type with good reduction outside finitely many places.
A theorem on bimeromorphic maps of K¨ ahle r manifolds and its applications
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Unpolarized Shafarevich conjectures for hyper-K\"ahler varieties
Proves finiteness of isomorphism classes of hyper-Kähler varieties in a given deformation type with good reduction outside finitely many places.