Three-dimensional affine quadric cone
= Three-dimensional affine quadric cone
{title2=$xy=zw$}
The <affine variety> $X=V(xy-zw)\subset\mathbb A^4$ has dimension three and a unique <singular point of an algebraic variety> at the origin. The planes $V_X(x,z)$ and $V_X(y,w)$ have dimension two but intersect only at that origin. This is a basic failure of <intersection dimension estimates> at singular points.