A probabilistic algorithm for the secant defect of Grassmann varieties
| dc.creator | McGillivray, Barbara | |
| dc.date | 2005-11-28 | |
| dc.date.accessioned | 2026-07-07T06:51:49Z | |
| dc.date.available | 2026-07-07T06:51:49Z | |
| dc.description | In this paper we study the higher secant varieties of Grassmann varieties in relation to Waring's problem for alternating tensors and to Alexander-Hirschowitz theorem. We show how to identify defective higher secant varieties of Grassmannians using a probabilistic method involving Terracini's Lemma, and we describe an algorithm which can compute, by numerical methods, dim(G(k,n)^{s}) for n<=14. Our main result is that, except for Grassmannians of lines, if n<=14 and k<=(n-1)/2 (if n=14 we have studied the case k<=5) there are only the four known defective cases: G(2,6)^{3}, G(3,7)^{3}, G(3,7)^{4} and G(2,8)^{4}. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0511683 | |
| dc.identifier | http://arxiv.org/abs/math/0511683 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105114 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14Q15 (Primary); 13P10; 15A69 (Secondary) | |
| dc.title | A probabilistic algorithm for the secant defect of Grassmann varieties | |
| dc.type | text |