An 𝔽
p2
-maximal Wiman sextic and its automorphisms
Keyword(s):
Abstract In 1895 Wiman introduced the Riemann surface 𝒲 of genus 6 over the complex field ℂ defined by the equation X 6+Y 6+ℨ 6+(X 2+Y 2+ℨ 2)(X 4+Y 4+ℨ 4)−12X 2 Y 2 ℨ 2 = 0, and showed that its full automorphism group is isomorphic to the symmetric group S 5. We show that this holds also over every algebraically closed field 𝕂 of characteristic p ≥ 7. For p = 2, 3 the above polynomial is reducible over 𝕂, and for p = 5 the curve 𝒲 is rational and Aut(𝒲) ≅ PGL(2,𝕂). We also show that Wiman’s 𝔽192 -maximal sextic 𝒲 is not Galois covered by the Hermitian curve H19 over the finite field 𝔽192 .
2009 ◽
Vol 05
(05)
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pp. 897-910
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1969 ◽
Vol 9
(1-2)
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pp. 109-123
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1979 ◽
Vol 27
(2)
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pp. 163-166
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1995 ◽
Vol 52
(2)
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pp. 209-225
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1998 ◽
Vol 124
(1)
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pp. 73-80
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Keyword(s):
1970 ◽
Vol 13
(1)
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pp. 95-97
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Keyword(s):
2006 ◽
Vol 182
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pp. 259-284
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