论文标题
非常对称的Hyper-Kähler四倍
Very symmetric hyper-Kähler fourfolds
论文作者
论文摘要
G.Höhn和G. Mason对所有有限组归类为忠实和符合性的hyper-k {ä} hler四倍的K3 $^{[2]} $。其中有15个最大值，称它们为$ \ widetilde {g} _1，\ ldots，\ widetilde {g} _ {15} $。类型K3 $^{[2]} $的每个流形都承认某些$ i $的$ \ widetilde {g} _i $的操作一定必须具有最大的Picard Rank 21。这一事实使我们可以使用晶格理论方法来对所有有限的组$ g $分类，忠实地在hyper-k {ä} hler type k3 $^{[2] $ x $ x $ typer of Type typer of Type of typer of K3 $^{[2]} $ g $ contrains $ g $ contrains $ \ wideTiLde {g} _i {g} _i $ syms $ sym $ sym $ sympl and $ wideteLlyty $ \ wideteLlytialde $ \ wideTilde} $ x $。我们还描述了K3 $^{[2]} $的四倍的示例 - 键入此类组的动作。
G. Höhn and G. Mason classified all finite groups acting faithfully and symplectically on a hyper-K{ä}hler fourfolds of type K3$^{[2]}$. There are 15 maximal among them, call them $\widetilde{G}_1,\ldots, \widetilde{G}_{15}$. Every manifold of type K3$^{[2]}$ admitting an action of $\widetilde{G}_i$ for some $i$ must necessarily have Picard rank 21 which is maximal. This fact allows us to use lattice-theoretic methods to classify all the finite groups $G$ acting faithfully on a hyper-K{ä}hler fourfold of type K3$^{[2]}$ $X$ such that $G$ contains $\widetilde{G}_i$ as a proper subgroup and $\widetilde{G}_i$ acts symplectically on $X$. We also describe examples of fourfolds of K3$^{[2]}$-type admitting an action of such groups.
