Real rank geometry of ternary forms
| Type of Publication: | Journal article |
| Publication status: | Published |
| URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-2-86nr32tvcafl2 |
| Author: | Michalek, Mateusz; Moon, Hyunsuk; Sturmfels, Bernd; Ventura, Emanuele |
| Year of publication: | 2017 |
| Published in: | Annali di Matematica Pura ed Applicata ; 196 (2017), 3. - pp. 1025-1054. - Springer. - ISSN 0373-3114. - eISSN 1618-1891 |
| DOI (citable link): | https://dx.doi.org/10.1007/s10231-016-0606-3 |
| Summary: |
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.
|
| Subject (DDC): | 510 Mathematics |
| Keywords: | Real rank, Ternary form, Discriminant |
| Link to License: | Attribution 4.0 International |
| Refereed: | Yes |
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MICHALEK, Mateusz, Hyunsuk MOON, Bernd STURMFELS, Emanuele VENTURA, 2017. Real rank geometry of ternary forms. In: Annali di Matematica Pura ed Applicata. Springer. 196(3), pp. 1025-1054. ISSN 0373-3114. eISSN 1618-1891. Available under: doi: 10.1007/s10231-016-0606-3
@article{Michalek2017-06geome-52492, title={Real rank geometry of ternary forms}, year={2017}, doi={10.1007/s10231-016-0606-3}, 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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