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At some point in this past year, some Fukaya people I know got very excited about the Fukaya categories of symplectic manifolds with "Lagrangian skeletons." As I understand it, a Lagrangian skeleton …

Kaledin and Verbitsky have shown that symplectic varities have a remarkably nice deformation theory as symplectic varieties. Let $X$ be a symplectic variety (a smooth quasi-projective variety over $\ …

This is a bit of a stab in the dark but I was wondering if anyone has defined cohomology classes on a hyperkähler manifold which pull back to the Stiefel-Whitney classes on any submanifold which is La …

This is one of these questions where it's tempting to just leave it at the title, but let me try to define the objects in question. A conical symplectic resolution is a projective resolution of singu …

Let $G$ be your favorite simple complex Lie group, and $P\subset G$ your favorite parabolic subgroup. We can identify $T^*G/P$ with the space of pairs $$\{(gP,x)\in G/P\times \mathfrak g | x\perp \o …

I'd really like to hear any references or information people have about the Fukaya categories of hyperkahler reductions of vector spaces (for more informations on the varieties, see Nick Proudfoot's t …

This is a somewhat speculative question, so bear with that (or not, as is your preference). Let $X$ be a smooth projective variety, and let $\omega_X$ be its canonical sheaf. The Euler class of th …

This is a follow-up to some earlier questions about flatness of schematic fixed points of certain deformations. Since I could never come up with good enough hypotheses in those examples, let me try a …