Fix a degree $d$ projective curve $X\subset {\mathbb{P}}^r$ over an algebraically closed field $K$. Let $U\subset {({\mathbb{P}}^r)}^{\ast }$ be a dense open subvariety such that every hyperplane $H\in U$ intersects $X$ in $d$ smooth points. Varying $H\in U$ produces the monodromy action $\phi :{\pi }_1^{\text{ét}}(U)\to S_d$. Let $G_X≔im(\phi )$. The permutation group $G_X$ is called the sectional monodromy group of $X$. In characteristic 0, $G_X$ is always the full symmetric group, but sectional monodromy groups in characteristic $p$ can be smaller. For a large class of space curves ( $r⩾3$), we classify all possibilities for the sectional monodromy group $G$ as well as the curves with $G_X=G$. We apply similar methods to study a particular family of rational curves in ${\mathbb{P}}^2$, which enables us to answer an old question about Galois groups of generic trinomials.

中文翻译：

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投影曲线的截面单峰组

修学位 $d$ 射影曲线 $X\subset {\mathbb{P}}^{\mathrm{[R}}$ 在代数封闭域上 $ķ$。让$ü\subset {（{\mathbb{P}}^{\mathrm{[R}}）}^{\ast }$ 是一个密集的开放子变量，这样每个超平面 $H\in ü$ 相交 $X$ 在 $d$平滑点。变化的$H\in ü$ 产生垄断行为 $\phi ：{\pi }_{\mathrm{1个}}^{\text{ét}}（ü）\to {\mathrm{小号}}_d$。让$G_X≔即时通讯（\phi ）$。排列组$G_X$ 被称为分区单峰集团 $X$。在特征0中，$G_X$ 始终是完全对称的基团，但特征上的截面单峰基团 $p$可以更小。对于一大类空间曲线（$\mathrm{[R}⩾3$），我们对分段单峰组的所有可能性进行了分类 $G$ 以及曲线 $G_X=G$。我们采用类似的方法来研究特定的有理曲线族${\mathbb{P}}^2$，这使我们能够回答有关通用三项式Galois组的一个旧问题。