Secant dimensions of low-dimensional homogeneous varieties

Abstract. We completely describe the higher secant dimensions of all con-nected 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 P1 × P1, P1 × P1 × P1, and P2 × P1, as well as for the variety F of incident point-line pairs in P2. For P2 × P1 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. 1. Introduction an