Veronese surface
= Veronese surface
{c}
{title2=$\nu_2(\mathbb P^2)\subseteq\mathbb P^5$}
The complete system of quadratic forms maps $\mathbb P^2$ to a smooth surface of degree four in $\mathbb P^5$. The six coordinates are $x_0^2,x_0x_1,x_0x_2,x_1^2,x_1x_2,x_2^2$. It occurs as a degree-two image of a <K3 surface> and, after taking a projective cone, in the plane-quintic exception to the <K3 linear system dichotomies>.