New examples of maximal curves with low genus

Daniele Bartoli, Massimo Giulietti, Motoko Kawakita, Maria Montanucci*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper, explicit equations for algebraic curves with genus 4, 5, and 10 already studied in characteristic zero, are analyzed in positive characteristic p. We show that these curves have an interesting behaviour on the number of their rational places. Namely, they are either maximal or minimal over the finite field with p2 elements for infinitely many p's. The key tool is the investigation of their Jacobian decomposition. Lists of small p's for which maximality holds are provided. In some cases we also describe the automorphism group of the curve.

Original languageEnglish
Article number101744
JournalFinite fields and their applications
Volume68
Number of pages32
ISSN1071-5797
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Algebraic curves
  • Finite fields
  • Maximal curves

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