Proves finiteness of isomorphism classes of hyper-Kähler varieties in a given deformation type with good reduction outside finitely many places.
Collections of or bits of hyperplane type in homogeneous spaces, homoge- neous dynamics, and hyperk¨ ahler geometry.International Mathematics Research Notices , page rnx319
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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.