On symplectic automorphisms of hyper-Kähler fourfolds of \(K3^{[2]}\) type (Q376666)
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scientific article; zbMATH DE number 6229185
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On symplectic automorphisms of hyper-Kähler fourfolds of \(K3^{[2]}\) type |
scientific article; zbMATH DE number 6229185 |
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On symplectic automorphisms of hyper-Kähler fourfolds of \(K3^{[2]}\) type (English)
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19 November 2013
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hyperkähler manifolds
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holomorphic symplectic structure
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\(K3\)
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symplectic automorphism
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The author proves that the symplectic automorphism group of \(K3^{[2]}\) is a subgroup of \(Co_1\), which is a subgroup of \(Co_0\). The definition of \(Co_0\) and \(Co_1\) could be found in [\textit{J. H. Conway} and \textit{N. J. A. Sloane}, Sphere packings, lattices and groups. Grundlehren der Mathematischen Wissenschaften. 290. New York, NY: Springer (1999; Zbl 0915.52003)] page 291.NEWLINENEWLINEIt is not clear whether the order of the automorphism could only be 11 other than order between 2 and 8 in [\textit{S. Mukai}, Invent. Math. 94, No. 1, 183--221 (1988; Zbl 0705.14045)], which comes from a \(K3\) surface. But he gave an example of order 11. The author should possibly at least state what is \(Co_1\).
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