On the ranks of the third secant variety of Segre–Veronese embeddings. Issue 3 (4th March 2019) - Ballico, Edoardo; Bernardi, Alessandra
Abstract: We give an upper bound for the rank of the border rank 3 partially symmetric tensors. In the special case of border rank 3 tensorsT ∈ V 1 ⊗ ⋯ ⊗ V k (Segre case) we can show that all ranks among 3 andk - 1 arise and ifdim V i ≥ 3 for all i 's, then all the ranks between k and2 k - 1 arise.