Joint differential invariants of binary and ternary forms

Gülden Gün Polat, Peter J. Olver

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2 Scopus citations


We use moving frames to construct and classify the joint invariants and joint differential invariants of binary and ternary forms. In particular, we prove that the differential invariant algebra of ternary forms is generated by a single third order differential invariant. To connect our results with earlier analysis of Kogan, we develop a general method for relating differential invariants associated with different choices of cross-section.

Original languageEnglish (US)
Pages (from-to)169-204
Number of pages36
JournalPortugaliae Mathematica
Issue number2
StatePublished - 2019

Bibliographical note

Funding Information:
Thanks to Irina Kogan for many helpful remarks and the referees for useful suggestions. G. G?n Polat acknowledges the support and hospitality during her stay at the University of Minnesota, where this work was initiated.The work of G. G?n Polat is supported by the Scientific and Technological Research Council of Turkey (TUBITAK). The work of P. J. Olver was partially supported by NSF grant DMS-1108894.

Publisher Copyright:
© 2019 European Mathematical Society.

Copyright 2020 Elsevier B.V., All rights reserved.


  • Binary form
  • Classical invariant theory
  • Differential invariant
  • Joint differential invariant
  • Joint invariant
  • Moving frame
  • Syzygy
  • Ternary form


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