论文标题
关于某些光滑投射品种的超平面部分的家族
On the families of hyperplane sections of some smooth projective varieties
论文作者
论文摘要
在本说明中，我们给出了\ cite [theorem 3.1] {hwang}的两个应用程序。我们首先研究了平滑hypersurface $ x \ subset \ subset \ mathbb {p}^{n+1} $ of度量$ d \ ge ge 3 $的免费家庭$ \ mathcal {k} $。我们证明$ x $由免费族$ \ Mathcal {k} $确定，如果$ \ dim（x）\ ge 4 $。作为一个应用程序，我们推断出，对于$ n \ ge 4 $，$ x $的超平面部分在$ \ mathbb {p}^n $的光滑高度$ d \ ge 3 $的模量空间中最大化。然后，我们研究了带有Kodaira dimension $κ（x）\ ge 0 $的光滑投射表面$ x $的超平面部分的免费家族。我们证明$ x $由这个免费家庭确定。
In this note, we give two applications of \cite[Theorem 3.1]{Hwang}. We first study the free family $\mathcal{K}$ of hyperplane sections of the smooth hypersurface $X\subset\mathbb{P}^{n+1}$ of degree $d\ge 3$. We prove that $X$ is determined by the free family $\mathcal{K}$ if $\dim(X)\ge 4$. As an application, we deduce that for $n\ge 4$, the hyperplane section of $X$ varies maximally in the moduli space of the smooth hypersurface of degree $d\ge 3$ in $\mathbb{P}^n$. We then study the free family of hyperplane sections of the smooth projective surface $X$ with Kodaira dimension $κ(X)\ge 0$. We prove that $X$ is determined by this free family.
