Secant varieties of segre–veronese varieties ℙm × ℙn embedded by o(1, 2)

Experimental Mathematics

Volumn 18, Issue 3, 2009, Pages 369-384

  Abo, Hirotachi ^a   Brambilla, Maria Chiara ^b  

^a UNIVERSITY OF IDAHO   (United States)

^b UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

Author keywords

Defectivity; Secant varieties; Segre Veronese varieties

Indexed keywords

EID: 70349925082     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2009.10129051     Document Type: Article

References (26)

1. H. Abo, G. Ottaviani, and C. Peterson. “Non-defectivity of Grassmannians of Planes.” arXiv:0901.2601, 2009.
2. H. Abo, G. Ottaviani, and C. Peterson. “Induction for Secant Varieties of Segre Varieties.” Trans. Amer. Math. Soc. 361: 2 (2009), 767–792.
3. S. Abrescia. “About Defectivity of Certain Segre–Veronese Varieties.” Canad. J. Math. 60: 5 (2008), 961–974.
4. J. Alexander and A. Hirschowitz. “Polynomial Interpolation in Several Variables.” J. Algebraic Geom. 4: 2 (1995), 201–222.
5. S. Aoki, T. Hibi, H. Ohsugi, and A. Takemura. “Markov Basis and Groebner Basis of Segre– Veronese Configuration for Testing Independence in Groupwise Selections.” arXiv:0704.1073, 2007.
6. E. Ballico. “On the Non-defectivity and Non Weak-Defectivity of Segre–Veronese Embeddings of Products of Projective Spaces.” Port. Math. 63: 1 (2006), 101–111.
7. K. Baur and J. Draisma. “Secant Dimensions of Low-Dimensional Homogeneous Varieties.” arXiv:0707.1605, 2007.
8. K. Baur, J. Draisma, and W. de Graaf. “Secant Dimensions of Minimal Orbits: Computations and Conjectures.” Experiment. Math. 16: 2 (2007), 239–250.
9. M. C. Brambilla and G. Ottaviani. “On the Alexander–Hirschowitz Theorem.” J. Pure and Applied Algebra 212: 5 (2008), 1229–1251.
10. P. Bürgisser, M. Clausen, and M. A. Shokrollahi. Algebraic Complexity theory, Grundl. Math. Wiss. 315. New York: Springer, 1997.
11. E. Carlini and M. V. Catalisano. “Existence Results for Rational Normal Curves.” J. Lond. Math. Soc. (2) 76: 1 (2007), 73–86.
12. E. Carlini and J. Chipalkatti. “On Waring’s Problem for Several Algebraic Forms.” Comment. Math. Helv. 78: 3 (2003), 494–517.
13. M.V. Catalisano, A. V. Geramita, and A. Gimigliano. “Ranks of Tensors, Secant Varieties of Segre Varieties and Fat Points.” Linear Algebra Appl. 355 (2002), 263–285
14. erratum, Linear Algebra Appl. 367 (2003), 347–348.
15. M. V. Catalisano, A. V. Geramita, and A. Gimigliano. “Higher Secant Varieties of Segre–Veronese Varieties.” In Projective Varieties with Unexpected Properties, pp. 81–107. Berlin: Walter de Gruyter, 2005.
16. 1 and Their Secant Varieties.” Collect. Math. 58: 1 (2007), 1–24.
17. M. V. Catalisano, A. V. Geramita, and A. Gimigliano. “On the Ideals of Secant Varieties to Certain Rational Varieties.” J. Algebra 319: 5 (2008), 1913–1931.
18. N. Eriksson, K. Ranestad, B. Sturmfels, and S. Sullivant. “Phylogenetic Algebraic Geometry.” In Projective Varieties with Unexpected Properties, pp. 237–255. Berlin: Walter de Gruyter, 2005.
19. L.D. Garcia, M. Stillman, and B. Sturmfels. “Algebraic Geometry of Bayesian Networks.” J. Symbolic Comput. 39: 3–4 (2005), 331–355.
20. J. M. Landsberg. “The Border Rank of the Multiplication of Two by Two Matrices Is Seven.” J. Amer. Math. Soc. 19 (2006), 447–459.
21. J. M. Landsberg. “Geometry and the Complexity of Matrix Multiplication.” Bull. Amer. Math. Soc. (N.S.) 45 (2008), 247–284.
22. G. Ottaviani. “Symplectic Bundles on the Plane, Secant Varieties and Lüroth Quartics Revisited.” To appear in Quaderni di Matematica, Proceedings of the School (and Workshop) on Vector Bundles and Low Codimensional Varieties, Trento 2006. Preprint, math.AG/0702151, 2006.
23. V. Strassen. “Rank and Optimal Computation of Generic Tensors.” Linear Algebra Appl. 52/53 (1983), 645–685.
24. B. Sturmfels and S. Sullivant. “Combinatorial Secant Varieties.” Pure Appl. Math. Q. 2: 3 (2006) 867–891.
25. S. Sullivant. “Combinatorial Symbolic Powers.” J. Algebra 319: 1 (2008), 115–142.
26. A. Terracini. “Sulle Vk per cui la varietà degli Sh (h + 1)-seganti ha dimensione minore dell’ordinario.” Rend. Circ. Mat. Palermo 31 (1911), 392–396.