Real rank geometry of ternary forms

Michalek, Mateusz; Moon, Hyunsuk; Sturmfels, Bernd; Ventura, Emanuele

Real rank geometry of ternary forms

Dateien

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Datum

2017

Autor:innen

Michalek, Mateusz

Moon, Hyunsuk

Sturmfels, Bernd

Ventura, Emanuele

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Annali di Matematica Pura ed Applicata. Springer. 2017, 196(3), pp. 1025-1054. ISSN 0373-3114. eISSN 1618-1891. Available under: doi: 10.1007/s10231-016-0606-3

Zusammenfassung

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Real rank, Ternary form, Discriminant

Zitieren

ISO 690

MICHALEK, Mateusz, Hyunsuk MOON, Bernd STURMFELS, Emanuele VENTURA, 2017. Real rank geometry of ternary forms. In: Annali di Matematica Pura ed Applicata. Springer. 2017, 196(3), pp. 1025-1054. ISSN 0373-3114. eISSN 1618-1891. Available under: doi: 10.1007/s10231-016-0606-3

BibTex

@article{Michalek2017-06geome-52492,
  year={2017},
  doi={10.1007/s10231-016-0606-3},
  title={Real rank geometry of ternary forms},
  number={3},
  volume={196},
  issn={0373-3114},
  journal={Annali di Matematica Pura ed Applicata},
  pages={1025--1054},
  author={Michalek, Mateusz and Moon, Hyunsuk and Sturmfels, Bernd and Ventura, Emanuele}
}

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