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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarting something, not done yet <a href="https://ncatlab.org/nlab/revision/compact+hyperk%C3%A4hler+manifold/1">v1</a>, <a href="https://ncatlab.org/nlab/show/compact+hyperk%C3%A4hler+manifold">current</a>

   starting something, not done yet

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 29th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave now added this statement and the respective references: The only known examples of [[compact hyperkähler manifolds]] are [[Hilbert schemes of points]] $X^{[n+1]}$ (for $n \in \mathbb{N}$) for $X$ either 1. a [[K3-surface]] 1. a [[4-torus]] (in which case the [[compact hyperkähler manifolds]] is really the [[fiber]] of $(\mathbb{T}^4)^{[n]} \to \mathbb{T}^4$) ([Beauville 83](#Beauville83)) and two exceptional examples ([O'Grady 99](#OGrady99), [O'Grady 03](#OGrady03) ), see [Sawon 04, Sec. 5.3](#Sawon04). <a href="https://ncatlab.org/nlab/revision/compact+hyperk%C3%A4hler+manifold/1">v1</a>, <a href="https://ncatlab.org/nlab/show/compact+hyperk%C3%A4hler+manifold">current</a>

   Have now added this statement and the respective references:

   The only known examples of compact hyperkähler manifolds are Hilbert schemes of points $X^{[n+1]}$ (for $n \in \mathbb{N}$) for $X$ either

   1. a K3-surface

   2. a 4-torus (in which case the compact hyperkähler manifolds is really the fiber of $(\mathbb{T}^4)^{[n]} \to \mathbb{T}^4$)

   (Beauville 83) and two exceptional examples (O’Grady 99, O’Grady 03 ), see Sawon 04, Sec. 5.3.

   v1, current