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^2Y^2Z^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 Kof 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 H192.
An Fp2-maximal Wiman sextic and its automorphisms
Giulietti M.
;
2021
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^2Y^2Z^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 Kof 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 H192.File in questo prodotto:
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