Linearly dependent and concise subsets of a Segre variety depending on $k$ factors
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We study linearly dependent subsets with prescribed cardinality $s$ of a multiprojective space. If the set $S$ is a circuit, there is an upper bound on the number of factors of the minimal multiprojective space containing $S$. B. Lovitz gave a sharp upper bound for this number. If $S$ has higher dependency, this may be not true without strong assumptions (and we give examples and suitable assumptions). We describe the dependent subsets $S$ with $\#S=6$.
Abstract
We study linearly dependent subsets with prescribed cardinality $s$ of a multiprojective space. If the set $S$ is a circuit, there is an upper bound on the number of factors of the minimal multiprojective space containing $S$. B. Lovitz gave a sharp upper bound for this number. If $S$ has higher dependency, this may be not true without strong assumptions (and we give examples and suitable assumptions). We describe the dependent subsets $S$ with $\#S=6$.
참고문헌 (10)
- E. Ballico, "Linearly dependent subsets of Segre varieties", Journal of Geometry, 111(2), pp.19~ (2020), Springer Science and Business Media LLC[DOI]
- Edoardo Ballico, "Stratification of the fourth secant variety of Veronese varieties via the symmetric rank", Advances in Pure and Applied Mathematics, 4(2), pp.215~250 (2013), ISTE Group[DOI]
- Edoardo Ballico, "Bounds on the tensor rank", Annali di Matematica Pura ed Applicata (1923 -), 197(6), pp.1771~1785 (2018), Springer Science and Business Media LLC[DOI]
- E. Ballico, "On the partially symmetric rank of tensor products of W-states and other symmetric tensors", Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl, 30(1), pp.93~124 (2019), European Mathematical Society - EMS - Publishing House GmbH[DOI]
- E. Ballico, "Identifiability of rank-3 tensors", arXiv:2001.10497, ~ (2001)
- R. Hartshorne, "Algebraic Geometry" (1977), Springer-Verlag
- J. W. P. Hirschfeld, "General Galois Geometries, Oxford Mathematical Monographs" (1991), The Clarendon Press, Oxford University Press
- W. C. Huffman, "Fundamentals of error-correcting codes" (2003), Cambridge University Press
- J. M. Landsberg, "Tensors: geometry and applications" (2012), American Mathematical Society
- B. Lovitz, "Toward a generalization of Kruskal’s decomposition on tensor decomposition", arXiv:1812.00264v2, ~