Secant dimensions of low-dimensional homogeneous varieties
We completely describe the higher secant dimensions of all connected homogeneous projective varieties of dimension at most 3, in all possible equivariant embeddings. In particular, we calculate these dimensions for all Segre-Veronese embeddings of P^1 * P^1, P^1 * P^1 * P^1, and P^2 * P^1, as well as for the variety F of incident point-line pairs in P^2. For P^2 * P^1 and F the results are new, while the proofs for the other two varieties are more compact than existing proofs. Our main tool is the second author's tropical approach to secant dimensions.
|Keywords||secant varieties, tropical geometry, polyhedral optimisation|
|MSC||Toric varieties, Newton polyhedra (msc 14M25), Polytopes and polyhedra (msc 52Bxx), Representation theory (msc 20G05)|
|THEME||Logistics (theme 3)|
|Publisher||Cornell University Library|
|Series||arXiv.org e-Print archive|
Baur, K, & Draisma, J. (2008). Secant dimensions of low-dimensional homogeneous varieties. arXiv.org e-Print archive. Cornell University Library .