Real rank geometry of ternary forms

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2017-06
Major/Subject
Mcode
Degree programme
Language
en
Pages
30
1-30
Series
ANNALI DI MATEMATICA PURA ED APPLICATA
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.
Description
Keywords
Discriminant, Real rank, Ternary form
Other note
Citation
Michałek , M , Moon , H , Sturmfels , B & Ventura , E 2017 , ' Real rank geometry of ternary forms ' , Annali di Matematica Pura ed Applicata , vol. 196 , no. 3 , pp. 1025–1054 . https://doi.org/10.1007/s10231-016-0606-3