Mathematics – Algebraic Geometry
Scientific paper
2007-07-11
Adv. Geom. 10 (2010), no. 1, 1-29
Mathematics
Algebraic Geometry
25 pages, many pictures
Scientific paper
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.
Baur Karin
Draisma Jan
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