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hyperkahler manifolds, complex Lagrangian submanifolds, Mukai flop, integrable systems

7 votes
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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
4 votes
0 answers
195 views

Deformation to a normal cone for a holomorphically symplectic manifold

Let $X$ be a subvariety in $M$. "Deformation to the normal cone" is a holomorphic deformation of a neighbourhood of $X$ in $M$ over the disk such that its central fiber is the total space of the norm …
Misha Verbitsky's user avatar