Real rank geometry of ternary forms

Mateusz Michałek; Hyunsuk Moon; Bernd Sturmfels; Emanuele Ventura

doi:10.1007/s10231-016-0606-3

Real rank geometry of ternary forms

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

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

21 Citations (Scopus)

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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
Pages (from-to)	1025–1054
Journal	Annali di Matematica Pura ed Applicata
Volume	196
Issue number	3
DOIs	https://doi.org/10.1007/s10231-016-0606-3
Publication status	Published - Jun 2017
MoE publication type	A1 Journal article-refereed

Keywords

Discriminant
Real rank
Ternary form

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10.1007/s10231-016-0606-3

10.1007_s10231-016-0606-3Final published version, 665 KBLicence: CC BY

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KW - Ternary form

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Real rank geometry of ternary forms

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Keywords

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