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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeDec 29th 2019

starting something, not done yet

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeDec 29th 2019

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 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.