Higher secant varieties of Segre-Veronese varieties
By M. Catalisano, A. V. Geramita, Alessandro Gimigliano. 2003
101 citations recorded by the source corpus.
We study the dimension of the higher secant varieties $X^s$ of ${\Bbb X} = {\Bbb P}^{n_1}\times ...\times {\Bbb P}^{n_t}$ embedded the morphism given by ${\cal O}_{\Bbb X}({a_1,...,a_t})$. We call it a {\it Segre-Veronese variety} and the embedding a {\it Segre-Veronese embedding}. In several cases (e.g. for 3 factors {\Bbb P}^{1}, or when $s$ is small) we show that $X^s$ has the expected dimension except for a few cases. A list of examples of defective $X^s$'s is given.
Subfields: Computational Mathematics
View Paper: https://www.semanticscholar.org/paper/0d3e2db9b4d3fc818be334af2ab7ed9f3efeb4b3
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In Computational Mathematics
- Alessandra Bernardi
- A. Oneto
- Alessandro Gimigliano
- Enrico Carlini
- M. Catalisano
- Seth Sullivant
- A. V. Geramita
- Bernd Sturmfels
Citations in the corpus
- On the first infinitesimal neighborhood of a linear configuration of points in P2 (2006, background): “[1], and K. Chandler [16] as well as that of Bocci [6], Catalisano, Geramita and Gimigliano [ 13 ], Ciliberto [17], Ciliberto and Miranda [18], [19], Gimigliano [35], Laface and Ugaglia [46], [47], Yang [57] and for further references see the survey article of Miranda [52] and since then - for large”
- On the dimensions of secant varieties of Segre-Veronese varieties (2009, unknown): “1 in [18] implies that T (1, 1; 2, 3; 3) and T (1, 1; 1, 3; 3) are true.”
- Combinatorial symbolic powers (2006, background): “gre product. Segre-Veronese varieties naturally generalize the Segre 20 SETH SULLIVANT varieties and Veronese varieties, and their secant varieties and symbolic powers pose many interesting questions [6]. The ideals of Segre-Veronese varieties are, in many cases, the ideals of 2 × 2 minors of certai”
- The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “First, in [99] and in [130], the cases of two and three copies of P1, respectively, were completely solved.”