Full metadata record
DC Field | Value | Language |
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dc.contributor.author | Buczyński, Jarosław | - |
dc.contributor.author | Han, Kang Jin | - |
dc.contributor.author | Mella, Massimiliano | - |
dc.contributor.author | Teitler, Zach | - |
dc.date.accessioned | 2018-04-11T03:46:33Z | - |
dc.date.available | 2018-04-11T03:46:33Z | - |
dc.date.created | 2018-03-29 | - |
dc.date.issued | 2018-03 | - |
dc.identifier.issn | 2199-675X | - |
dc.identifier.uri | http://hdl.handle.net/20.500.11750/6156 | - |
dc.description.abstract | Given a closed subvariety X in a projective space, the rank with respect to X of a point p in this projective space is the least integer r such that p lies in the linear span of some r points of X. Let Wk be the closure of the set of points of rank with respect to X equal to k. For small values of k such loci are called secant varieties. This article studies the loci Wk for values of k larger than the generic rank. We show they are nested, we bound their dimensions, and we estimate the maximal possible rank with respect to X in special cases, including when X is a homogeneous space or a curve. The theory is illustrated by numerous examples, including Veronese varieties, the Segre product of dimensions (1,3,3), and curves. An intermediate result provides a lower bound on the dimension of any GLn orbit of a homogeneous form. © 2017, The Author(s). | - |
dc.language | English | - |
dc.publisher | Springer Nature | - |
dc.title | On the locus of points of high rank | - |
dc.type | Article | - |
dc.identifier.doi | 10.1007/s40879-017-0172-2 | - |
dc.identifier.scopusid | 2-s2.0-85042701842 | - |
dc.identifier.bibliographicCitation | European Journal of Mathematics, v.4, no.1, pp.113 - 136 | - |
dc.description.isOpenAccess | TRUE | - |
dc.subject.keywordAuthor | Rank locus | - |
dc.subject.keywordAuthor | Secant variety | - |
dc.subject.keywordAuthor | Symmetric tensor rank | - |
dc.subject.keywordAuthor | Tensor rank | - |
dc.citation.endPage | 136 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 113 | - |
dc.citation.title | European Journal of Mathematics | - |
dc.citation.volume | 4 | - |