 Quadric (algebraic geometry)

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.

In algebraic geometry, a quadric refers to a specific type of algebraic variety defined by a homogeneous polynomial of degree two. These varieties can be studied in various contexts, typically as subsets of projective or affine spaces.