论文标题
K3表面具有命令4的符合性自动形态
K3 surfaces with a symplectic automorphism of order 4
论文作者
论文摘要
给定的$ x $ a k3表面承认订单4的符号自动形态$τ$，我们描述了$ h^2（x，\ mathbb z）$上的等距$τ^*$。在分别调用$ \ tilde z $和$ \ tilde y $之后，商表面的最低分辨率$ z = x/τ^2 $和$ y = x/τ$，我们还描述了共同体在合理商$ x \ rightarrow z \ rightarrow z，\ x \ x \ right的地图中引起的地图y \ rightArrow \ tilde z $：据此，我们能够给出$ \ tilde Z $的晶格理论表征，并找到$ x，\ tilde Z $和$ \ tilde y $的Néron-Severi lattices之间的关系。我们还为$ x，\ tilde z $和$ \ tilde y $生产了三种不同的投影模型，每个模型都与$ x $上的4度的两极分化相关。
Given $X$ a K3 surface admitting a symplectic automorphism $τ$ of order 4, we describe the isometry $τ^*$ on $H^2(X,\mathbb Z)$. Having called $\tilde Z$ and $\tilde Y$ respectively the minimal resolutions of the quotient surfaces $Z=X/τ^2$ and $Y=X/τ$, we also describe the maps induced in cohomology by the rational quotient maps $X\rightarrow\tilde Z,\ X\rightarrow\tilde Y$ and $\tilde Y\rightarrow\tilde Z$: with this knowledge, we are able to give a lattice-theoretic characterization of $\tilde Z$, and find the relation between the Néron-Severi lattices of $X,\tilde Z$ and $\tilde Y$ in the projective case. We also produce three different projective models for $X,\tilde Z$ and $\tilde Y$, each associated to a different polarization of degree 4 on $X$.
