  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.
