Real rank geometry of ternary forms
| dc.contributor | Aalto-yliopisto | fi |
| dc.contributor | Aalto University | en |
| dc.contributor.author | Michałek, Mateusz | |
| dc.contributor.author | Moon, Hyunsuk | |
| dc.contributor.author | Sturmfels, Bernd | |
| dc.contributor.author | Ventura, Emanuele | |
| dc.contributor.department | Polish Academy of Sciences | |
| dc.contributor.department | Korea Advanced Institute of Science and Technology | |
| dc.contributor.department | University of California Berkeley | |
| dc.contributor.department | Department of Mathematics and Systems Analysis | |
| dc.date.accessioned | 2016-10-13T06:10:42Z | |
| dc.date.issued | 2017-06 | |
| dc.description.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. | en |
| dc.description.version | Peer reviewed | en |
| dc.format.extent | 30 | |
| dc.format.extent | 1-30 | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.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 | en |
| dc.identifier.doi | 10.1007/s10231-016-0606-3 | |
| dc.identifier.issn | 0373-3114 | |
| dc.identifier.other | PURE UUID: a27b89b6-2b42-4734-b66b-8a4dea334952 | |
| dc.identifier.other | PURE ITEMURL: https://research.aalto.fi/en/publications/a27b89b6-2b42-4734-b66b-8a4dea334952 | |
| dc.identifier.other | PURE LINK: http://www.scopus.com/inward/record.url?scp=84983465338&partnerID=8YFLogxK | |
| dc.identifier.other | PURE FILEURL: https://research.aalto.fi/files/14981359/10.1007_s10231_016_0606_3.pdf | |
| dc.identifier.uri | https://aaltodoc.aalto.fi/handle/123456789/22930 | |
| dc.identifier.urn | URN:NBN:fi:aalto-201610135030 | |
| dc.language.iso | en | en |
| dc.relation.ispartofseries | ANNALI DI MATEMATICA PURA ED APPLICATA | en |
| dc.rights | openAccess | en |
| dc.subject.keyword | Discriminant | |
| dc.subject.keyword | Real rank | |
| dc.subject.keyword | Ternary form | |
| dc.title | Real rank geometry of ternary forms | en |
| dc.type | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä | fi |
| dc.type.version | publishedVersion |