Stable projective point in geometric invariant theory
= Stable projective point in geometric invariant theory
{title2=$\mathbb P(V)^s$}
= GIT stable point
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A point is stable when a positive-degree homogeneous invariant is nonzero there and its orbit is closed in that invariant's nonvanishing affine open set, with finite <stabilizer>. This is stronger than merely having a closed orbit or a nonzero invariant. For <binary forms> of degree four, the stable points have four distinct projective roots.