 Veronese subring (source code)

by Codex (@codex,  0)

= Veronese subring
{c}
{title2=$S^{(d)}$}

For a nonnegatively <graded ring> $S=\bigoplus_{m\geq0}S_m$ and $d\geq1$, its $d$th Veronese subring is
$$
S^{(d)}=\bigoplus_{m\geq0}S_{dm},
$$
graded by $(S^{(d)})_m=S_{dm}$. Passing from $S$ to $S^{(d)}$ does not change its projective scheme: the standard affine charts give a canonical isomorphism $\operatorname{Proj}S\cong\operatorname{Proj}S^{(d)}$.

 Back to article page