Abstract
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 language | English |
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Pages (from-to) | 1025–1054 |
Journal | Annali di Matematica Pura ed Applicata |
Volume | 196 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jun 2017 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Discriminant
- Real rank
- Ternary form