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.
Additional Metadata
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 De Gruyter
Journal Advances in Geometry
Citation
Baur, K, & Draisma, J. (2010). Secant dimensions of low-dimensional homogeneous varieties. Advances in Geometry, 10(0707.1605), 1–29.