On the ranks of the third secant variety of Segre-Veronese embeddings

2017/01/24 by Ballico, Edoardo, Bernardi, Alessandra
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1701.06845

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 tensors T∈ V₁⊗ ⋯ ⊗ V_k (Segre case) we can show that all ranks among 3 and k-1 arise and if dim V_i ≥ 3 for all i's, then also all the ranks between k and 2k-1 arise.

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