Finiteness of isomorphism classes of generic fibers in pointed locally trivial families of Q-factorial terminal primitive symplectic varieties with fixed special fiber, plus projective finiteness under semi-ampleness, with optimality via explicit infinite families.
The unpolarized Shafarevich Conjecture for K3 Surfaces
2 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We prove the unpolarized Shafarevich conjecture for K3 surfaces: the set of isomorphism classes of K3 surfaces over a fixed number field with good reduction away from a fixed and finite set of places is finite. Our proof is based on the theorems of Faltings and Andr\'e, as well as the Kuga-Satake construction.
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UNVERDICTED 2representative citing papers
Proves finiteness of isomorphism classes of hyper-Kähler varieties in a given deformation type with good reduction outside finitely many places.
citing papers explorer
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Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture
Finiteness of isomorphism classes of generic fibers in pointed locally trivial families of Q-factorial terminal primitive symplectic varieties with fixed special fiber, plus projective finiteness under semi-ampleness, with optimality via explicit infinite families.
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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.