Real rank geometry of ternary forms

Mateusz Michałek*, Hyunsuk Moon, Bernd Sturmfels, Emanuele Ventura

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

16 Citations (Scopus)
274 Downloads (Pure)


We study real ternary forms whose real rank equals the generic complex rank, and we characterize the semialgebraic set of sums of powers representations with that rank. Complete results are obtained for quadrics and cubics. For quintics, we determine the real rank boundary: It is a hypersurface of degree 168. For quartics, sextics and septics, we identify some of the components of the real rank boundary. The real varieties of sums of powers are stratified by discriminants that are derived from hyperdeterminants.

Original languageEnglish
Pages (from-to)1025–1054
JournalAnnali di Matematica Pura ed Applicata
Issue number3
Publication statusPublished - Jun 2017
MoE publication typeA1 Journal article-refereed


  • Discriminant
  • Real rank
  • Ternary form


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