An Fp2-maximal Wiman sextic and its automorphisms

Massimo Giulietti*, Motoko Kawakita, Stefano Lia, Maria Montanucci

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In 1895 Wiman introduced the Riemann surface W of genus 6 over the complex field C defined by the equation X6+Y6+Z6+(X2+Y2+Z2)(X4+Y4+Z4)-12X2Y2Z2 = 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.

Original languageEnglish
JournalAdvances in Geometry
Volume21
Issue number4
Pages (from-to)451-461
ISSN1615-715X
DOIs
Publication statusPublished - 1 Oct 2021

Bibliographical note

Publisher Copyright:
© 2021 Walter de Gruyter GmbH, Berlin/Boston.

Keywords

  • Hermitian curve
  • Maximal curve
  • Quotient curves
  • Unitary groups
  • Wiman's sextic

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