We present a fine-structure entanglement classification under stochastic
local operation and classical communication (SLOCC) for multiqubit pure states.
To this end, we employ specific algebraic-geometry tools that are SLOCC
invariants, secant varieties, to show that for $n$-qubit systems there are
$\lceil\frac{2^{n}}{n+1}\rceil$ entanglement families. By using another
invariant, $\ell$-multilinear ranks, each family can be further split into a
finite number of subfamilies. Not only does this method facilitate the
classification of multipartite entanglement, but it also turns out to be
operationally meaningful as it quantifies entanglement as a resource.
