Irrelevant ideal of projective space
= Irrelevant ideal of projective space
{title2=$S_+$}
In the standard graded <homogeneous coordinate ring> $S=k[x_0,\ldots,x_n]$ of $\mathbb P^n$, the irrelevant ideal is
$$
S_+=(x_0,\ldots,x_n).
$$
It vanishes only at the origin of the corresponding <affine cone>, which does not represent a <projective point>.
It is the polynomial-ring instance of the <irrelevant ideal of a graded ring>.