= Affine null cone
{title2=$\mathcal N_G(V)=\{v:0\in\overline{Gv}\}$}
The <affine null cone> is the set of vectors whose orbit closure contains the origin. For a reductive algebraic group it is also the common zero locus of all positive-degree homogeneous invariants. A nonzero vector in this set represents an unstable projective point. The <Hilbert-Mumford criterion for the affine null cone> detects membership by a <algebraic one-parameter subgroup> with only positive active weights.
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