On the identifiability of binary Segre products

Journal of Algebraic Geometry

Volumn 22, Issue 1, 2013, Pages 1-11

  Bocci, Cristiano ^a   Chiantini, Luca ^a  

^a UNIVERSITY OF SIENA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84875132172     PISSN: 10563911     EISSN: None     Source Type: Journal    
DOI: 10.1090/S1056-3911-2011-00592-4     Document Type: Article

References (16)

1. H. Abo, G. Ottaviani, C. Peterson, Induction for secant varieties of Segre varieties, Trans. Amer. Math. Soc. 361(2009), 767-792. MR2452824 (2010a:14088)
2. B. Adlansdvik, Joins and Higher secant varieties, Math. Scand. 61(1987), 213-222. MR947474 (89j:14030)
3. E. S. Allman, C. Matias, J. A. Rhodes, Identifiability of parameters in latent structure models with many observed variables. Ann. Statist. 37(2009), 3099-3132. MR2549554 (2010m:62029)
4. C. Bocci, L. Chiantini, Appendix to "On the identifiability of binary Segre products", Available at: www.mat.unisi.it/personalpages/ chiantini/p1app.pdf.
5. M. V. Catalisano, A. V. Geramita, A. Gimigliano, Ranks of tensors, secant varieties of Segre varieties and fat points, Linear Algebra Appl. 355(2002), 263-285. MR1930149 (2003g:14070)
6. 1) (n-times) are NOT Defective for n ≥ 5, J. Algegraic Geom. 20(2011), 295-327. MR2762993
7. L. Chiantini, C. Ciliberto, Weakly defective varieties, Trans. Amer. Math. Soc. 354(2002), 151-178. MR1859030 (2003b:14063)
8. L. Chiantini, C. Ciliberto, On the classification of defective threefolds, in Projective Varieties with Unexpected Properties, Proceedings of the Siena Conference, C. Ciliberto, A. V. Geramita, B. Harbourne, R. M. Mirò-Roig, K. Ranestad, ed., W. de Gruyter (2005), 131-176. MR2202251 (2006k:14068)
9. L. Chiantini, C. Ciliberto, On the concept of k-secant order of a variety, J. London Math. Soc. 73(2006), 436-454. MR2225496 (2007k:14110) (Pubitemid 43665856)
10. C. Ciliberto, M. Mella, F. Russo, Varieties with one apparent double point, J. Algebraic Geom. 13(2004), 475-512. MR2047678 (2005b:14078) (Pubitemid 38727111)
11. M. Dale, Terracini's lemma and the secant variety of a curve, Proc. London Math. Soc. 49(1984), 329-339. MR748993 (85g:14066)
12. R. Elmore, P. Hall, A. Neeman, An application of classical invariant theory to identifiability in non-parametric mixtures, Ann. Inst. Fourier 55(2005), 1-28. MR2141286 (2006m:62056)
13. D. Grayson, M. Stillman, Macaulay 2, a software system for research in algebraic geometry, Available at: www.math.uiuc.edu/Macaulay2/.
14. J. B. Kruskal, Three-way arrays: rank and uniqueness of trilinear decompositions, with applications to arithmetic complexity and statistics, Lin. Alg. Applic. 18(1977), 95-138. MR0444690 (56:3040)
15. h, (h+1)-seganti ha dimensione minore dell'ordinario, Rend. Circ. Mat. Palermo 31(1911), 392-396.
16. F. L. Zak, Tangents and secants of varieties, AMS Bookstore publications, Transl. Math. Monog. 127 (1993). MR1234494 (94i:14053)