Journal article
M. Giulietti, M. Kawakita, Stefano Lia, M. Montanucci
Advances in Geometry, 2021
Advances in Geometry, 2021
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APA
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Giulietti, M., Kawakita, M., Lia, S., & Montanucci, M. (2021). An π½p2-maximal Wiman sextic and its automorphisms. Advances in Geometry.
Chicago/Turabian
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Giulietti, M., M. Kawakita, Stefano Lia, and M. Montanucci. βAn π½p2-Maximal Wiman Sextic and Its Automorphisms.β Advances in Geometry (2021).
MLA
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Giulietti, M., et al. βAn π½p2-Maximal Wiman Sextic and Its Automorphisms.β Advances in Geometry, 2021.
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@article{m2021a,
title = {An π½p2-maximal Wiman sextic and its automorphisms},
year = {2021},
journal = {Advances in Geometry},
author = {Giulietti, M. and Kawakita, M. and Lia, Stefano and Montanucci, M.}
}
Abstract
Abstract In 1895 Wiman introduced the Riemann surface π² of genus 6 over the complex field β defined by the equation X6+Y6+β¨6+(X2+Y2+β¨2)(X4+Y4+β¨4)β12X2Y2β¨2 = 0, and showed that its full automorphism group is isomorphic to the symmetric group S5. We show that this holds also over every algebraically closed field π of characteristic p β₯ 7. For p = 2, 3 the above polynomial is reducible over π, and for p = 5 the curve π² is rational and Aut(π²) β PGL(2,π). We also show that Wimanβs π½192-maximal sextic π² is not Galois covered by the Hermitian curve H19 over the finite field π½192.
