English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We determine the possible finite groups $G$ of symplectic automorphisms of hyperkahler manifolds which are deformation equivalent to the second Hilbert scheme of a K3 surface. We prove that $G$ has such an action if, and only if, it is isomorphic to a subgroup of either the Mathieu group $M_{23}$ having at least four orbits in its natural permutation representation on $24$ elements, or one of two groups $3^{1+4}{:}2.2^2$ and $3^4{:}A_6$ associated to $\mathcal{S}$-lattices in the Leech lattice. We describe in detail those $G$ which are maximal with respect to these properties, and (in most cases) we determine all deformation equivalence classes of such group actions. We also compare our results with the predictions of Mathieu Moonshine.

Finite groups of symplectic automorphisms of hyperkahler manifolds of type K3