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By using invariant theory we show that a (higher-dimensional) Lorentzianmetric that is not characterised by its invariants must be of aligned type II;i.e., there exists a frame such that all the curvature tensors aresimultaneously of type II. This implies, using the boost-weight decomposition,that for such a metric there exists a frame such that all positive boost-weightcomponents are zero. Indeed, we show a more general result, namely that any setof tensors which is not characterised by its invariants, must be of alignedtype II. This result enables us to prove a number of related results, amongthem the algebraic VSI conjecture.

A spacetime not characterised by its invariants is of aligned type II