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- W2891720151 abstract "Fix a degree $d$ projective curve $X subset mathbb{P}^r$ over an algebraically closed field $K$. Let $U subset (mathbb{P}^r)^*$ 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 $varphi: pi_1^{text{'et}}(U) to S_d$. Let $G_X := mathrm{im}(varphi)$. The permutation group $G_X$ is called the sectional monodromy group of $X$. In characteristic zero $G_X$ is always the full symmetric group, but sectional monodromy groups in characteristic $p$ can be smaller. For a large class of space curves ($r geqslant 3$) 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." @default.
- W2891720151 created "2018-09-27" @default.
- W2891720151 creator A5077194193 @default.
- W2891720151 date "2020-09-07" @default.
- W2891720151 modified "2023-10-16" @default.
- W2891720151 title "Sectional monodromy groups of projective curves" @default.
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- W2891720151 doi "https://doi.org/10.1112/jlms.12375" @default.
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