论文标题
不变的司曼尼人和K3表面，其作用为192*2
Invariant Grassmannians and a K3 surface with an action of order 192*2
论文作者
论文摘要
考虑到有限尺寸的复杂矢量空间$ v $，其Grassmannian品种参数为给定维度的$ V $的所有子空间。同样，如果有限的$ g $在$ v $上表现出来，其不变的格拉曼尼亚人会参数给定维度的$ v $的所有$ g $ invariant子空间。基于这一事实，我们开发了一种用于计算$ g $ invariant投射品种的算法，该品种是相同程度的超出表面的交集。 我们应用该算法来找到一个偏光K3表面的投射模型，其忠实的动作为$ t_ {192} \rtimesμ_2$，以及一些具有8度极化的进一步的对称K3表面。
Given a complex vector space $V$ of finite dimension, its Grassmannian variety parametrizes all subspaces of $V$ of a given dimension. Similarly, if a finite group $G$ acts on $V$, its invariant Grassmannian parametrizes all the $G$-invariant subspaces of $V$ of a given dimension. Based on this fact, we develop an algorithm for computing $G$-invariant projective varieties arising as an intersection of hypersurfaces of the same degree. We apply the algorithm to find a projective model of a polarized K3 surface with a faithful action of $T_{192}\rtimes μ_2$ and some further symmetric K3 surfaces with a degree 8 polarization.
