Set-theoretic defining equations of the tangential variety of the Segre variety

Journal of Pure and Applied Algebra

Volumn 215, Issue 6, 2011, Pages 1516-1527

  Oeding, Luke ^a  

^a UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79551471521     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2010.09.009     Document Type: Article

References (25)

1. Borodin A., Rains E. Eynard-Mehta theorem, Schur process, and their Pfaffian analogs. J. Stat. Phys. 2005, 121:291-317.
2. M.V. Catalisano, A. Geramita, A. Gimigliano, Secant Varieties of (P1)×...×(P1) (n-times) are NOT Defective for n≥5, 2008.
3. Drton M., Sturmfels B., Sullivant S. Lectures on algebraic statistics. Oberwolfach Seminars 39 2009, Birkhäuser, Basel, viii, 271~p.
4. Drton M., Sturmfels B., Sullivant S. Algebraic factor analysis: tetrads, pentads and beyond. Probab. Theory Related Fields 2007, 138:463-493.
5. Fulton W., Harris J. Representation Theory: A First Course. Graduate Texts in Mathematics 1991, vol. 129. Springer-Verlag, New York.
6. Garcia L., Stillman M., Sturmfels B. Algebraic geometry of Bayesian networks. J. Symbolic Comput. 2005, 39:331-355.
7. B. Georgi, Context-specific independence mixture models for cluster analysis of biological data, Ph.D. thesis, Universität Berlin, 2009.
8. Georgi B., Schliep A. Context-specific independence mixture modeling for positional weight matrices. Bioinformatics 2006, 22. e166-173.
9. D.R. Grayson, M.E. Stillman, Macaulay2, a software system for research in algebraic geometry, Available at:, 2010. http://www.math.uiuc.edu/Macaulay2/.
10. Griffin K., Tsatsomeros M. Principal minors. II. The principal minor assignment problem. Linear Algebra Appl. 2006, 419:125-171.
11. Holtz O., Sturmfels B. Hyperdeterminantal relations among symmetric principal minors. J. Algebra 2007, 316:634-648.
12. J.M. Landsberg, The Geometry of Tensors with Applications, 2010 (in preparation).
13. Landsberg J.M., Manivel L. On the ideals of secant varieties of Segre varieties. Found. Comput. Math. 2004, 4:397-422.
14. Landsberg J.M., Manivel L. Construction and classification of complex simple Lie algebras via projective geometry. Selecta Math. (N.S.) 2002, 8:137-159.
15. J.M. Landsberg, Z. Teitler, On the ranks and border ranks of symmetric tensors, 2009.
16. Landsberg J.M., Weyman J. On tangential varieties of rational homogeneous varieties. J. Lond. Math. Soc. (2) 2007, 76:513-530.
17. Lin S., Sturmfels B. Polynomial relations among principal minors of a 4×4-matrix. J. Algebra 2009, 322:4121-4131.
18. L. Oeding, G-varieties and the principal minors of symmetric matrices, Ph.D. thesis, Texas A&M University, 2009.
19. L. Oeding, Set-theoretic defining equations of the variety of principal minors of symmetric matrices, 2009. Preprint: arxiv:0809.4236.
20. Pachter L., Sturmfels B. Algebraic Statistics for Computational Biology 2005, Cambridge University Press, New York.
21. Vandebril R., Golub G., Van~Barel M. A quasi-separable approach to solve the symmetric definite tridiagonal generalized eigenvalue problem. SIAM J. Matrix Anal. Appl. 2009, 31:154-174.
22. Vandebril R., Van Barel M., Mastronardi N. Linear systems. Matrix Computations and Semiseparable Matrices. Vol. 1 2008, Johns Hopkins University Press, Baltimore, MD.
23. Weyman J. Cohomology of Vector Bundles and Syzygies. Cambridge Tracts in Mathematics 2003, vol. 149. Cambridge University Press.
24. Zak F.L. Tangents and Secants of Algebraic Varieties. Translations of Mathematical Monographs 1993, vol. 127. American Mathematical Society, Providence, Translated from the Russian manuscript by the author.
25. Zamarashkin N.L., Oseledets I.V., Tyrtyshnikov E.E. The tensor structure of the inverse of a Toeplitz band matrix. Dokl. Akad. Nauk 2009, 428:161-162.