论文标题
小属的K3表面上的理性曲线
Rational curves on K3 surfaces of small genus
论文作者
论文摘要
令$ \ mathfrak b_g $表示原始两极分化的$ k3 $表面$（s，h）$ g $ g $ ive $ \ m athbb c $的模量空间。众所周知，$ \ Mathfrak b_g $是不可约的，对于任何原始的极化$ k3 $ surface $（s，h）$，只有$ | h | $有限的理性曲线。因此，我们可以提出找到此类曲线的单型组的问题。 $ g = 2 $的情况基本上是从哈里斯\ cite {ha}的结果中遵循的，它是完整的对称组$ s_ {324} $，在这里我们解决了案例$ g = 3 $和$ 4 $。
Let $\mathfrak B_g$ denote the moduli space of primitively polarized $K3$ surfaces $(S,H)$ of genus $g$ over $\mathbb C$. It is well-known that $\mathfrak B_g$ is irreducible and that there are only finitely many rational curves in $|H|$ for any primitively polarized $K3$ surface $(S,H)$. So we can ask the question of finding the monodromy group of such curves. The case of $g=2$ essentially follows from the results of Harris \cite{Ha} to be the full symmetric group $S_{324}$, here we solve the case $g=3$ and $4$.
