论文标题
高度超曲面的线性切片的模量
Moduli of linear slices of high degree hypersurfaces
论文作者
论文摘要
我们研究了$ \ mathbb {p}^n $中Hypersurfaces线性部分的变化。我们完全对所有平面曲线进行了分类，必须是单数，其线段在模量中不会最大变化。在较高的维度中，我们证明了$ \ mathbb {p}^n $ in $ \ mathbb {p}^n $的超平面部分的家族对$ d \ geq n+3 $的最大变化。在此过程中，我们概括了经典的Grauert-Mulich定理，涉及投射空间中的线条，既可以在投影空间中的$ k $ stranes，又可以在任意品种上自由理性曲线。
We study the variation of linear sections of hypersurfaces in $\mathbb{P}^n$. We completely classify all plane curves, necessarily singular, whose line sections do not vary maximally in moduli. In higher dimensions, we prove that the family of hyperplane sections of any smooth degree $d$ hypersurface in $\mathbb{P}^n$ vary maximally for $d \geq n+3$. In the process, we generalize the classical Grauert-Mulich theorem about lines in projective space, both to $k$-planes in projective space and to free rational curves on arbitrary varieties.
