Veronese embedding
= Veronese embedding
{c}
{title2=$\nu_d$}
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The degree-$d$ Veronese embedding sends a <projective point> to all monomials of degree $d$ in its homogeneous coordinates. For example,
$$
\nu_2:\mathbb P^1\longrightarrow\mathbb P^2,
\qquad [x:y]\longmapsto[x^2:xy:y^2],
$$
is a closed immersion with image the conic $uw-v^2=0$.