Sectional monodromy groups of projective curves

@article{Kadets2018SectionalMG,
  title={Sectional monodromy groups of projective curves},
  author={Borys Kadets},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
  • Borys Kadets
  • Published 2018
  • Mathematics
  • arXiv: Algebraic Geometry
  • 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… CONTINUE READING
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