K3 surfaces with a symplectic automorphism of order 11
K3 surfaces with a symplectic automorphism of order 11
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具有 11 阶辛自同构的 K3 曲面
DOI：
10.4171/jems/167
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发表时间：
2006
影响因子：
2.6
通讯作者：
J. Keum
中科院分区：
文献类型：
--
作者：
I. Dolgachev;J. Keum
我们分类可能的有限群的辛自同构的K3曲面的顺序可被11整除。地面场的特性必须等于11。这类群的完整列表由五个群组成：11阶循环群，$11\rtimes 5$，$L_2（11）$和Mathieu群$M_{11}$，$M_{22}$。我们还表明，表面$X$承认的自同构$g$的顺序11承认一个$g $不变的椭圆纤维化的雅可比纤维化同构的显式给定的椭圆K3表面之一。
We classify possible finite groups of symplectic automorphisms of K3 surfaces of order divisible by 11. The characteristic of the ground field must be equal to 11. The complete list of such groups consists of five groups: the cyclic group of order 11, $11\rtimes 5$, $L_2(11)$ and the Mathieu groups $M_{11}$, $M_{22}$. We also show that a surface $X$ admitting an automorphism $g$ of order 11 admits a $g$-invariant elliptic fibration with the Jacobian fibration isomorphic to one of explicitly given elliptic K3 surfaces.