Questions tagged [hyperkaehler]
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8
votes
0answers
158 views
Hyperkähler structure on the moduli space of tetrahedra?
Consider a moduli space of geodesic tetrahedra in the hyperbolic space $\mathbb{H}^3.$ In the Klein's model the hyperbolic space can be presented as the interior of a unit ball
$$
\mathbb{H}^3=\{(x_1,...
4
votes
1answer
68 views
Lagrangian cores of quiver variety in different GIT chambers
Let $\pi: \mathfrak{M}_{(\theta,0)}(Q,\text{v},\text{w}) \rightarrow \mathfrak{M}_{(0,0)}(Q,\text{v},\text{w})$ be the projective morphism between Nakajima quiver varieties when complex moment ...
1
vote
1answer
99 views
Small contraction for Hyperkähler Varieties
I have the following basic question. Everything is over $\mathbb{C}$.
Let $X$ be a hyperkähler (irreducible holomorphic symplectic) variety and we consider a small contraction $f\colon X \rightarrow ...
1
vote
1answer
125 views
compact manifold as a hyperkahler quotient of an infinite-dimensional affine space
Is it possible to obtain K3 (or any other compact
hyperkahler manifold) with its hyperkahler structure
as a hyperkahler quotient of an infinite-dimensional affine
quaternionic vector space with an ...
6
votes
1answer
315 views
Are there non-projective, but algebraic, hyperkahler varieties?
Let $k$ be an algebraically closed field of characteristic zero. I am not sure what the right definition of a hyperkahler variety over $k$ is, but I think the following might be close enough.
...
0
votes
0answers
74 views
Extending Beauville-Bogomolov orthogonal decomposition from variety to scheme
I'm seeking to understand the de Rham cohomology of a Hilbert scheme $K3^{[4]}$ of the K3 surface. By Beauville, this 8-dimensional compact manifold is Kaehler, irreducible, holomorphically symplectic ...
1
vote
0answers
86 views
Integral cohomology on compact irreducible holomorphic symplectic manifolds
In particular, I'm attempting to understand the integral cohomology on K3^[4], a Hilbert scheme on the projective K3 surface, and whether or not this compact Kaehler manifold admits a Kaehler form ...
4
votes
0answers
73 views
Different components of real sections for twistor spaces of hyper-Kähler manifolds
A hyper-Kähler manifold is a Riemannian manifold $(M,g)$ equipped with 3 complex structures $I,J,K$ obeying the quaternionic relations and such that $g$ is a Kähler metric for each complex structure. ...
2
votes
0answers
81 views
How exactly are holomorphic maps with hyperkahler targets identified as triholomorphic maps?
In Appendix A of Hyperinstantons, the Beltrami Equation, and Triholomorphic Maps by Fre et al., it is described how holomorphic maps from a Riemann surface to a hyperkahler manifold $\mathcal{N}$, ...
2
votes
1answer
138 views
Are there hyperkahler manifolds with multi-isotropic hyperkahler submanifolds?
This is a continuation of this question. As explained in the comments, for a hyperkaehler manifold $X$, a multi-isotropic submanifold $S$ has the property that the three distinguished Kahler forms $\...
2
votes
1answer
133 views
Submanifold of a Hyperkahler manifold which is 'Lagrangian' w.r.t. all three symplectic structures
Let $X$ be a hyperkaehler manifold. Being hyperkaehler, it has three distinguished Kaehler forms, $\omega^u$ ($u$=1,2,3), corresponding to its three distinguished almost complex structures.
How does ...
1
vote
1answer
156 views
Do these definitions of integrable quaternionic structure agree?
I have found two different definitions for integrable quaternionic structure in the literature, and I need to know if they agree with one another.
One definition that I have found (from Differential ...
