Secant dimensions of lowdimensional homogeneous varieties
Abstract
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 SegreVeronese 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 pointline 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2007
 arXiv:
 arXiv:0707.1605
 Bibcode:
 2007arXiv0707.1605B
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Representation Theory;
 14M25;
 52B99;
 20G05
 EPrint:
 25 pages, many pictures