Quadric (algebraic geometry)
= Quadric
{disambiguate=algebraic geometry}
{title2=$V(Q_2)\subseteq\mathbb P^N$}
{wiki}
= Quadric hypersurface
{synonym}
A projective hypersurface defined by a nonzero homogeneous quadratic form. Over $\mathbb C$, diagonalization identifies its rank; it is smooth when the rank is $N+1$ and otherwise is a cone with a linear vertex.