  We propose a new approach to the geometry of the four-qubit entanglement
classes depending on parameters. More precisely, we use invariant theory and
algebraic geometry to describe various stratifications of the Hilbert space by
SLOCC invariant algebraic varieties. The normal forms of the four-qubit
classification of Verstraete {\em et al.} are interpreted as dense subsets of
components of the dual variety of the set of separable states and an algorithm
based on the invariants/covariants of the four-qubit quantum states is proposed
to identify a state with a SLOCC equivalent normal form (up to qubits
permutation).
