The moduli space of binary quintics

Andrew du Plessis, Charles Terence Clegg Wall*

*Corresponding author for this work

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We recall the classical construction and theory of invariants for the case of binary quintics, describe the moduli space, and identify the curves in it defined by quintics having symmetry. We describe the real case, and identify the number of real roots depending on the point in moduli space. Our main interest is in five curves of binary quintics defined as linear sections of plane curves with infinite symmetry groups: these play a role in the canonical stratification of jet space, so we describe their singularities and count their intersections. All this is done in the classical case. Thereafter we analyse the changes to be made to the whole theory when we work in characteristic 2.

Original languageEnglish
JournalEuropean Journal of Mathematics
Pages (from-to)423-436
Number of pages14
Publication statusPublished - 1 Mar 2018


  • Binary quintics
  • Invariants
  • Moduli space
  • Stratification
  • Symmetries


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