论文标题
K3表面上最大模量的曲线
Curves of maximal moduli on K3 surfaces
论文作者
论文摘要
我们证明，如果$ x $是一个复杂的投射K3表面和$ g> 0 $，那么$ x $上的曲线属于$ x $的曲线，具有最大的曲线，即Moduli中的$ g $ diquiliation。特别是每个K3表面都包含几何属1的曲线，该曲线在非异常家族中移动。这意味着在恒定循环曲线上的huybrechts的猜想，并给出了Kobayashi定理的代数几何证明，即K3表面没有全局的对称差分形式。
We prove that if $X$ is a complex projective K3 surface and $g>0$, then there exist infinitely many families of curves of geometric genus $g$ on $X$ with maximal, i.e., $g$-dimensional, variation in moduli. In particular every K3 surface contains a curve of geometric genus 1 which moves in a non-isotrivial family. This implies a conjecture of Huybrechts on constant cycle curves and gives an algebro-geometric proof of a theorem of Kobayashi that a K3 surface has no global symmetric differential forms.
