Abstract
We study complex projective plane curves with a given group of automorphisms. Let $G$ be a simple primitive subgroup of $\mathrm{PGL}(3, \mathbf{C})$, which is isomorphic to $\mathfrak{A}_{6}$, $\mathfrak{A}_{5}$ or $\mathrm{PSL}(2, \mathbf{F}_{7})$. We obtain a necessary and sufficient condition on $d$ for the existence of a nonsingular projective plane curve of degree $d$ invariant under $G$. We also study an analogous problem on integral curves.
Acknowledgment
I am greatful to Associate Professor Takeshi Harui for useful discussions and the method of calculations. I would like to thank Associate Professor Nobuyoshi Takahashi for detailed advice in this paper.
Citation
Yusuke Yoshida. "Projective plane curves whose automorphism groups are simple and primitive." Kodai Math. J. 44 (2) 334 - 368, June 2021. https://doi.org/10.2996/kmj44208
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