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Jan 14, 2011 at 2:33 comment added Ben Webster Ah, sorry, didn't see "hyperkahler" mentioned in the question. Still, it's worth noting that "hyperkahler" doesn't have to only be a differential geometric notion. It can sneak back into algebraic geometry (even over finite fields!).
Jan 13, 2011 at 23:21 comment added Qfwfq * question .
Jan 13, 2011 at 23:18 comment added Qfwfq Yea. I knew it should correspond to holomorphic symplectic manifolds (perhaps "irreducible"?) and there is a whole $\mathbb{P}^1$ of such complex structures.. But what I was looking for in my answer was a bit more "à la Grothendieck": i.e. some spaces "over $\mathbb{H}$" in some suitable sense. (holom sympl manif's are definitely "over $\mathbb{C}$")
Jan 13, 2011 at 19:20 history answered Ben Webster CC BY-SA 2.5