Higher secant varieties of the Segre varieties

By M. Catalisano, A. V. Geramita, Alessandro Gimigliano. 2005

58 citations recorded by the source corpus.

Subfields: Computational Mathematics, Pathology and Forensic Medicine

View Paper: https://www.semanticscholar.org/paper/d888e62a93dbb4f2137209b81881a52f952261e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

In Pathology and Forensic Medicine

Jan Draisma

Citations in the corpus

The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “2), as in [22, 103], to translate the problem of determining the dimensions of the higher secant varieties of Xn,d into that of calculating the value, at d = (d1, .”
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem (2006, unknown): “dk, the determination of the generic outer product rank is an open problem in general and a nontrivial problem even in simple cases — see [13, 14] for results over C and [72, 73] for results over R.”
A tropical approach to secant dimensions (2006, background): “Also, I give a nice proof that the 6-fold Segre power of the projective line is non-defective; this cannot be proved using rook coverings alone, and is the first case not covered by [10].”
Identifiability of parameters in latent structure models with many observed variables (2008, unknown): “1016/S0024-3795(02)00352-X [8] Catalisano, M.”
Induction for secant varieties of Segre varieties (2006, background): “e recently this topic appears, through its relationship with algebraic statistics and higher order correlations, in connection with computational biology ([ERSS]). The special case X = P1 × ... × P1 ([CGG2]) has made several appearances in the recent physics literature (see for example [LT] and the ”
A Bayesian information criterion for singular models (2013, background): “However, theorem 2.3 in Catalisano et al. (2005) guarantees that all models in our simulation study below have dimension given by expression (6.14).”
Bounded-rank tensors are defined in bounded degree (2011, background): “Tensor rank is an important notion in such diverse areas as multilinear algebra and algebraic geometry [10, 11, 25]; algebraic statistics [1, 17], in particular with applications to phylogenetics [2, 9, 8, 30], and complexity theory [6, 7, 14, 21, 22, 23, 28, 29].”