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for questions about deformation theory, including deformations of manifolds, schemes, Galois representations, and von Neumann algebras.

7 votes
Accepted

Is the generic deformation of a symplectic variety affine?

Being "affine" in this case does not make much sense, because the hyperkaehler deformation is a complex manifold, without a fixed algebraic structure. Simpson produced an example of a hyperkaehler …
Misha Verbitsky's user avatar
1 vote
Accepted

Can deformation equivalent Kähler manifolds always be obtained by a deformation where all th...

I don't think this is known. For hyperkahler manifolds, conjecturally, all smooth complex deformations are class C and birational to hyperkahler. If this is true, your conjecture would follow automati …
Misha Verbitsky's user avatar