Secant dimensions of low-dimensional homogeneous varieties

Details Secant dimensions of low-dimensional homogeneous varieties Secant dimensions of low-dimensional homogeneous varieties

2007-07-11

arxiv.org/abs/0707.1605v1

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.

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