Fp2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve

Daniele Bartoli*, Maria Montanucci, Fernando Torres

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Let f be the finite field of order q2. It is sometimes attributed to Serre that any curve F-covered by the Hermitian curve Hq+1 : Yq+1 = xq + x is also F-maximal. For prime numbers q we show that every F-maximal curve X of genus g ≤ 2 with | Aut(X) | > 84(g - 1) is Galois-covered by Hq+1. The hypothesis on | Aut(X) | is sharp, since there exists an F-maximal curve X for q = 71 of genus g = 7 with | Aut(X) | = 84(7 - 1) which is not Galois-covered by the Hermitian curve H72.

Original languageEnglish
JournalAdvances in Geometry
Volume21
Issue number3
Pages (from-to)325-336
ISSN1615-715X
DOIs
Publication statusPublished - 1 Jul 2021

Bibliographical note

Publisher Copyright:
© 2021 De Gruyter. All rights reserved.

Keywords

  • Finite field
  • Galois-covering
  • Hermitian curve
  • Maximal curve

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