On partial and generic uniqueness of block term tensor decompositions

We present several conditions for generic uniqueness of tensor decompositions of multilinear rank (1,L_{1}, L_{1}),…, (1, L_{R}, L_{R}) terms. In geometric language, we prove that the joins of relevant subspace varieties are not tangentially weakly defective. We also give conditions for partial uniqueness of block term tensor decompositions by proving that the joins of relevant subspace varieties are not defective.